if x and y are 2 positive real numbers such that x²+4x²=17 and xy=2 then find the value of (x+2y)
ananya48:
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x² + 4y² = 17 and xy = 2 ⇒ y = 2/x
so x² + 4 (2/x)² = 17 ⇒ x⁴ + 16 - 17x² = 0
= x⁴ -17x² +16 = 0 ⇒ x⁴ -16x² - x² + 16 = 0 ⇒ (x² -16) (x² -1 ) = 0
that gives x = -1 , 1 , - 4 , 4 and so y = -2, 2 , -1/2 , 1/2
hope its right
so x² + 4 (2/x)² = 17 ⇒ x⁴ + 16 - 17x² = 0
= x⁴ -17x² +16 = 0 ⇒ x⁴ -16x² - x² + 16 = 0 ⇒ (x² -16) (x² -1 ) = 0
that gives x = -1 , 1 , - 4 , 4 and so y = -2, 2 , -1/2 , 1/2
hope its right
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