( a ^ { 5 }) ^ { x } = ( { 1 } /{ a ^ { 10 } } ) ^ { y } = a \sqrt{ a } , a \neq 0 \Rightarrow x ^ { 2 } + 4 y ^ { 2 } =

TS ICET 2017 Question Paper with Solutions for online practice

Question : 76 of 200

Marks: +1, -0

( a ^ { 5 }) ^ { x } = ( { 1 } /{ a ^ { 10 } } ) ^ { y } = a √{ a } , a ≠ 0 ⇒ x ^ { 2 } + 4 y ^ { 2 } =

Solution:

(a^{5})^{x}=({1}/{a^{10}})^{y}=a√{a}

⇒a^{5x}=a^{-10y}=a^{3/2}

⇒5x=3/{2}⇒x={3}/{10}

And

-10y={3}/{2}⇒y={-3}/{20}

⇒{x}^{2}+4{y}^{2}={9}/{100}+4×{9}/{400}=2×{9}/{100}={9}/{50}

xy=({3}/{10})(-{3}/{20})=-{9}/{200}

⇒x^{2}+4y^{2}=-4xy

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