Math, asked by asmaa31, 1 year ago

Please solve this.................​

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Answered by abhi178
0

answer : option (b) 1/2(b - a)

explanation : given, 1/a² - 1/b² = 1/c and ab = √c (where, c > 0 and a < b )

now, 1/a² - 1/b² = 1/c

or, 1/a² - 1/b² = 1/(√c)²

or, 1/a² - 1/b² = 1/a²b² [ given ab = √c ]

or, (b² - a²)/a²b² = 1/a²b²

or, (b² - a²) = 1

or, (b - a)(b + a) = 1 [ from algebraic identity, (x² - y²) = (x - y)(x + y) ]

or, (b + a) = 1/(b - a)......(1)

now, average value of a and b = (a + b)/2

from equation (1),

= 1/2(b - a)

hence, option (B) is correct choice.

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