Let p and q be two positive number such that


Let $p$ and $q$ be two positive number such that $p+q=2$ and $p^{4}+q^{4}=272 .$ Then $p$ and $q$ are roots of the equation :

  1. (1) $x^{2}-2 x+2=0$

  2. (2) $x^{2}-2 x+8=0$

  3. (3) $x^{2}-2 x+136=0$

  4. (4) $x^{2}-2 x+16=0$

Correct Option: , 4


$\left(p^{2}+q^{2}\right)^{2}-2 p^{2} q^{2}=272$

$\left((p+q)^{2}-2 p q\right)^{2}-2 p^{2} q^{2}=272$

$16+16 p q+2 p^{2} q^{2}=272$

$(p q)^{2}-8 p q-128=0$

$\mathrm{pq}=\frac{8 \pm 24}{2}=16,-8$



$x^{2}-(p+q) x+p q=0$

$x^{2}-2 x+16=0$

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