Question

If p SQUARE + q SQUARE + r SQUARE = 20 and pq + qr + rs = 15, then the value of p + q + r is

Answer 1

Answer:

$\textsf{The value of p+q+r is 5\sqrt{2} }$

Step-by-step explanation:

$\textsf{Given:}$

$\mathsf{p^2+q^2+r^2=20}$

$\mathsf{pq+qr+rp=15}$

$\textsf{Using the algebraic identity}$

$\boxed{\mathsf{(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)}}$

$\mathsf{(p+q+r)^2=p^2+q^2+r^2+2(pq+qr+rp)}$

$\mathsf{(p+q+r)^2=20+2(15)}$

$\mathsf{(p+q+r)^2=20+30}$

$\mathsf{(p+q+r)^2=50}$

$\mathsf{p+q+r=\sqrt{50}}$

$\implies\boxed{\mathsf{p+q+r=5\sqrt{2}}}$

Answer 2

Answer:

I think this is the best answer