Please solve this.................
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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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