Question

If p,q,r,s are in continued proportion prove that (p2+q2+r2)(q2+r2+s2)=(pq+qr+rs)2

Answer 1

Answer:

LHS = RHS

Step-by-step explanation:

p q r s are in continued proportion

Let say x is common factor

p = p

q = px

r = px²

s = px³

To Prove

(p² + q² + r²)(q² + r² + s²) = (pq + qr + rs)²

LHS

= (p² + (px)² + (px²)²)((px)² + (px²)² + (px³)²)

= (p² + p²x² + p²$x^4$)(p²x² + p²$x^4$ + p²$x^6$)

= p²(1 + x² + $x^4$)p²x²(1 + x² + $x^4$)

= $p^4$x²(1 + x² + $x^4$)²

=  (p²x)²(1 + x² + $x^4$)²

= ((p²x)(1 + x² + $x^4$))²

RHS

(pq + qr + rs)²

=(ppx +pxpx² +px²px³)²

= ((p²x)(1 + x² + $x^4$))²

Hence LHS = RHS

Answer 2

Answer:

LHS=RHS

Step-by-step explanation:

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