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it is known that the sum of a + b is
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equal to the product of a * B and is
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also equal to the quotient of a / B find
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a and b as usual before watching further
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pause and try to solve the problem on
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your own this equation is equivalent to
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a system of three equations the sum of a
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+ b is equal to the product of a * B the
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product is equal to the quotient and the
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sum is equal to the quotient let's start
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solving the system with the second
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equation considering that b is not equal
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to Z multiply both sides of the equation
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by B then a * b^ 2 = a move everything
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to the left side and factor out the
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common term the product of two factors
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is zero when at least one of them is
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equal to zero moving the negative - 1 to
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the right in the second equation we find
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that either a = 0 or B = plus or -1
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let's examine each of the three cases
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separately case one a equal 0
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substituting the value of a in the
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system we get 0 + B = 0 * B 0 * B = 0
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ided by B and 0 + B should equal 0 / B
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from the the first equation B must be
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equal to zero from the second equation B
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must not equal Z from the third equation
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B must be equal to zero but it must also
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not be equal to zero at the same time
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this system has no solution therefore in
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the first case when a equals z the
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solution case 2 B = -1 substituting into
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the system we get a -1 = a * -1 which =
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a from the second equation a = a
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/1 which also equals a from the third
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equation a - 1 must equal a / -1 which
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again equals a in the first equation
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move a to the left and -1 to the right
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resulting in 2 a equal 1 the second
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equation is true for any value of a the
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third equation gives the same result as
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the first therefore we get only one
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equation 2 a = 1 so a must equal 1
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12 if b equal -1 then a must be 1 12
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case 3 b equals 1 the system now looks
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like this a + 1 = a a * 1 = a / 1 which
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equals A and A + 1 = a / 1 which again
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equals a the first and third equations
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identical the second equation is true
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for any value of a moving a to the left
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and 1 to the right gives a - A = -1
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which means 0 must equal -1 which is not
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true therefore when b equals 1 the
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system like in the first case has no
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Solutions as a result we found that only
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one pair of numbers satisfies the system
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a = 12 and B = -1 write the answer a =
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12 and b equal -1 the problem is solved
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if you understood the solution give a
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thumbs up leave a comment and don't
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forget to subscribe to the channel
