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Question
If `bb(a/b = 2/3)` then find the value of the following expression.
`[5a^2 + 2b^2]/[ 5a^2 - 2b^2]`
Solution
`a/b = 2/3`
Squaring both sides,
⇒ `a^2/b^2 = 4/9`
⇒ `(5a^2)/(2b^2) = [5 xx 4]/[2 xx 9]`
⇒ `(5a^2)/(2b^2) = 20/18`
Applying componendo and dividendo, we get
`[5a^2 + 2b^2]/[ 5a^2 - 2b^2] = [20+18]/[20-18]`
⇒ `[5a^2 + 2b^2]/[ 5a^2 - 2b^2] = [38]/[2]`
⇒ `[5a^2 + 2b^2]/[ 5a^2 - 2b^2] = 19`
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