Question

plzz solve this urgent h
Mark one
if any one give me answer first I will Mark him brillianist

Answer 1

☺️☺️HEY MATE! HERE'S YOUR ANSWER!☺️☺️

rationalizing of p is done in attachment!

then, rationalizing of q will be done in same way ,

so, q = (7+3√5)/2

then,

$p + q = \frac{7 - 3 \sqrt{5} }{2} + \frac{7 + 3 \sqrt{5} }{2}$

$p + q = \frac{7 - 3 \sqrt{5} + 7 + 3 \sqrt{5} }{2}$

$p + q = \frac{14}{2} \\ \\ p + q =7$

then,

$(p + q)^{2} = {p}^{2} + {q}^{2} + 2(p)(q)$

$(7)^{2} = p^{2} + {q}^{2} + 2(\frac{7 - 3 \sqrt{5} }{2} \times \frac{7 + 3 \sqrt{5} }{2})$

$49 = {p}^{2} + {q}^{2} + 2(\frac{ ({7})^{2} - (3 \sqrt{5}) ^{2} }{4})$

$49 = {p}^{2} + {q}^{2} + 2( \frac{49 - 45}{2} )$

$49 = {p}^{2} + {q}^{2} + 2 \times \frac{4}{4}$

${p}^{2} + {q}^{2} = 49 - 2 = 47$

hope it is helpful ✌️!