(a+b):(a-b)=17: 1 then find the value of (a²-b²):(a²+b²)

Correct Answer is : 17:14517: 14517:145

Correct Answer is : 17:14517: 14517:145

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AFCAT I 12 Feb 2022 Shift 1 Paper

Question : 66 of 100

Marks: +1, -0

(a+b):(a-b)=17: 1

(a^2-b^2):(a^2+b^2)

Solution: 👈: Video Solution

Given

(a+b):(a-b)=17: 1

Formula Used:

a^2-b^2=(a-b)(a+b)

Calculation

(a+b):(a-b)=17: 1

Let

(a+b)=17 x \;\; \cdots (1)

And

(a-b)=x \;\; \cdots - (2)

Adding (1) and (2), we get

\Rightarrow 2 a = 18 x

\Rightarrow a = 9 x

Put the value of a in eq.(1), we get

\Rightarrow 9 x + b = 17 x

\Rightarrow b = 8 x

(a^2-b^2):(a^2+b^2)=[(9 x)^2-(8 x)^2]:[(9 x)^2+(8 x)^2]

\Rightarrow 17 x^2 : 145 x^2 = 17 : 145

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