Question

hlo preparation for exam help with this question?? °_*!
If p/q=q/r then prove that
p3+q3+r3=(1/p3+1/q3+1/r3)p2q2r2 ​

Answer 1

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Doubt clarification - use comment section.

Answer 2

The equation $p^3+q^3+r^3=(\frac{1}{p^3}+\frac{1}{q^3}+\frac{1}{r^3})p^2q^2r^2$ has been proved to be true

The equation is given as:

$\frac pq = \frac qr$

Cross multiply

$pr = q^2$

Rewrite as:

$q^2 = pr$

Also, we have:

$p^3+q^3+r^3=(\frac{1}{p^3}+\frac{1}{q^3}+\frac{1}{r^3})p^2q^2r^2$

Substitute $q^2 = pr$

$p^3+q^3+r^3=(\frac{1}{p^3}+\frac{1}{q^3}+\frac{1}{r^3})p^3r^3$

Expand

$p^3+q^3+r^3=\frac{1}{p^3} \times p^3r^3 +\frac{1}{q^3} \times p^3r^3 +\frac{1}{r^3} \times p^3r^3$

Simplify

$p3+q3+r3=r^3 +\frac{1}{q^3} \times p^3r^3 + p^3$

Rewrite as:

$p3+q3+r3=r^3 +\frac{1}{q^3} \times (pr)^3 + p^3$

Substitute $pr = q^2$

$p3+q3+r3=r^3 +\frac{1}{q^3} \times (q^2)^3 + p^3$

$p3+q3+r3=r^3 +\frac{1}{q^3} \times q^6 + p^3$

Divide q^6 by q^3

$p3+q3+r3=r^3 +q^3 + p^3$

Rewrite the equation as:

$p3+q3+r3=p^3 +q^3 + r^3$

Hence, the equation has been proved

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