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Question
Solve the following quadratic equations by factorization:
(a + b)2x2 - 4abx - (a - b)2 = 0
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Solution
We have been given
(a + b)2x2 - 4abx - (a - b)2 = 0
(a + b)2x2 - (a + b)2x + (a - b)2x - (a - b)2 = 0
(a + b)2x(x - 1) + (a - b)2(x - 1) = 0
((a + b)2x + (a - b)2)(x - 1) = 0
Therefore,
(a + b)2x + (a - b)2 = 0
(a + b)2x = - (a - b)2
`x=-((a-b)/(a+b))^2`
or,
x - 1 = 0
x = 1
Hence, `x=-((a-b)/(a+b))^2` or x = 1
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