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Question
If a : b = 9 : 10, find the value of `(2a^2 - 3b^2)/(2a^2 + 3b^2)`
Solution
a : b = 9 : 10
⇒ `a/b = (9)/(10)`
`(2a^2 - 3b^2)/(2a^2 + 3b^2)`
= `((2a^2)/(b^2) - (3b^2)/(b^2))/((2a^2)/(b^2) - (3b^2)/(b^2))` ...(Dividing by b2)
= `(2(a/b)^2 - 3)/(2(a/b)^2 + 3`
= `(2(9/10)^2 - 3)/(2(9/10)^2 + 3)`
= `(2 xx 81/100 - 3)/(2 xx 81/100 + 3)`
= `(81/50 - 3)/(81/50 + 3)`
= `((81 - 150)/(50))/((81 + 150)/(50)`
= `(-69)/(50) xx (50)/(231)`
= `(-69)/(231)`
= `(-23)/(77)`.
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