If p and q are real number such that p + q = 3 , p 4 + q 4 = 369 , then the value of 1 p + 1 q - 2 is equal to

Question

If p and q are real number such that p + q = 3 , p 4 + q 4 = 369 , then the value of 1 p + 1 q - 2 is equal to,

MARKS App · Accepted Answer

Given, p 4 + q 4 = 369 ⇒ p 2 + q 2 2 - 2 p q 2 = 369 ⇒ p + q 2 - 2 p q 2 - 2 p q 2 = 369 ⇒ 9 - 2 p q 2 - 2 p q 2 = 369 ⇒ p q 2 - 18 p q - 144 = 0 ⇒ p q = 24 ( rejected ) , - 6 Now, 1 p + 1 q - 2 = p q 2 p + q 2 = p q 2 9 = 4

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