Let p and q be two positive numbers such that p + q = 2 and p 4 + q 4 = 272 . Then p and q are roots of the equation:

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Aicharya · Accepted Answer

Consider p 2 + q 2 2 - 2 p 2 q 2 = 272 p + q 2 - 2 p q 2 - 2 p 2 q 2 = 272 16 - 16 p q + 2 p 2 q 2 = 272 p q 2 - 8 p q - 128 = 0 p q 2 - 8 p q - 128 = 0 p q = 8 &#177; 24 2 = 16 , - 8 &#8756; &#160;&#160; p q = 16 &#8756; &#160;&#160; Required equation : &#160; x 2 - 2 x + 16 = 0

Let p and q be two positive numbers such that p + q = 2 and p 4 + q 4 = 272 . Then p and q are roots of the…

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