Question

If p +q =13 and pq =22, then find the value of p4 + q4

Answer 1

★Given :

p+q = 13

pq = 22

★To find:

the value of p⁴ + q⁴

★Solution :

We know that,

${\pink{\boxed{(a+b)^2 = a^2+b^2+2ab}}}$

$(p+q)^2 = p^2+q^2+2pq \\ \\ \\ by\: putting\:the\:values\\ \\ \\ (13)^2 = p^2+q^2 +2(22) \\ \\ \\ 169 = p^2+q^2+44 \\ \\ \\p^2 + q^2 = 169 - 44 \\ \\ \\{\boxed{p^2+q^2 = 125}} \\ \\ \\ (p^2+q^2)^2 = p^4+q^4 + 2(p^2\times q^2) \\ \\ \\ {\blue{\boxed{Law - \:a^m \times b^m = (ab)^m}}} \\ \\ \\ (p^2+q^2)^2 = p^4+q^4 + 2(pq)^2 \\ \\ \\ by\: putting\: values$

$(125)^2 = p^4 + q^4 +2(22 \times 22) \\ \\ \\ 15625 = p^4+q^4 + 2(484) \\ \\ \\p^4+q^4 = 15625 - 968 \\ \\ \\ {\purple{\boxed{p^4+q^4 = 14,567}}}$

Answer 2

Answer:

$\large\boxed{p^4+q^4=14657}$

Step-by-step explanation:

Given:-

Values of p+q and pq are 13 and 22 respectively.

To Find:-

p⁴+q⁴= ?

Formula Applied:-

(a+b)²=a²+2ab+b²

[(a)²+(b)²] ²= (a)⁴+(b)⁴+2×(a²)×(b²)

Solution:-

p+q=13

Squaring both the sides:-

⇒ (p+q)²=(13)²

⇒ p²+q²+2pq=169

⇒ p²+q²+2(22)=169                      [∵pq=22]

⇒ p²+q²=169-44

⇒ p²+q²=125

Again, Squaring Both Sides:-

⇒ (p²+q²)²=(125)²

⇒ p⁴+q⁴+2(pq)²=15625

⇒ p⁴+q⁴+2(22)²=15625

⇒ p⁴+q⁴=15625-968

$\implies \large\boxed{p^4+q^4=14657}$

∴ The Value of p⁴+q⁴ is 14657.