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प्रश्न
If a, b, c and d are in proportion, the value of `(8a^2 - 5b^2)/(8c^2 - 5d^2)` is equal to ______.
विकल्प
a2 : b2
a2 : c2
a2 : d2
c2 : d2
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उत्तर
If a, b, c and d are in proportion, the value of `(8a^2 - 5b^2)/(8c^2 - 5d^2)` is equal to a2 : c2.
Explanation:
Since a, b, c and d are in proportion
∴ a : b :: c : d
`\implies a/b = c/d = k` ...(Say)
`\implies` a = bk and c = dk
`(8a^2 - 5b^2)/(8c^2 - 5d^2) = (8b^2k^2 - 5b^2)/(8d^2k^2 - 5d^2)`
= `(b^2(8k^2 - 5))/(d^2(8k^2 - 5))`
= `b^2/d^2`
= `(a/k)^2/(c/k)^2`
= `(a^2/k^2)/(c^2/k^2)`
= `a^2/c^2`
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