Question
If 2a + b = 15 and ab = 18, then the value of (4a² - b²)
.Solution
We know that, (x - y) 2 = (x + y) 2 - 4xy
So, (2a - b) 2 = (2a + b) 2 - 4 X 2ab
= 15 2 - 8 X 18 = 225 – 144 = 81
So, we can say that, (2a - b) = - 9, or, 9.
Since, all the given options are positive, so we will consider the positive value of (2a - b) , as (2a + b) is given positive.
We know that, x 2 - y 2 = (x + y) X (x - y)
So, 4a² - b² = (2a) 2 - b 2 = (2a + b) X (2a - b) = 15 X 9 = 135
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