STATEMENT-1: If x 2 y 3 = 6 , x 0 , y 0 then the least value of 3 x + 4 y is 10. STATEMENT-2: Least value of 3 x + 4 y occurs when 9 x = 8 y .

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STATEMENT-1: If x 2 y 3 = 6 , x > 0 , y > 0 then the least value of 3 x + 4 y is 10. STATEMENT-2: Least value of 3 x + 4 y occurs when 9 x = 8 y .

TestHub · Accepted Answer

Consider 2 3 ​ x \& 3 4 ​ y having weights 2 \& 3 respectively: 5 3 x + 4 y ​ ≥ ( 4 9 x 2 ​ ⋅ 27 64 y 3 ​ ) 1/5 = ( 4 9 ​ ⋅ 27 64 ​ ⋅ 2 6 ​ ) 1/5 ⋅ … ≥ 2 ⇒ 3 x + 4 y ≥ 10 . The least value occurs when 2 3 x ​ = 3 4 y ​ ⇒ 9 x = 8 y .

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