Question

If q is the mean proportion between p and r , Prove that
p² - q² + r² = q⁴(1/p² - 1/q² + 1/r²)​

Answer 1

Step-by-step explanation:

Question:- If q is the mean proportion between p and r , Prove that

p² - q² + r² = q⁴(1/p² - 1/q² + 1/r²)

Solution:-

Since, q is the mean proportional of p and r.

Hence, q² = pr

R.H.S. = q⁴[1/p² – 1/q²2 + 1/r²]

= q⁴[1/p² – 1/pr + 1/r²]

= q⁴[r² – pr + p²/p²r²]

= q²[p² – pr + r²/(pr)²]

= q⁴[p² – pr + r²/q⁴]

= p² – pr + r² = L.H.S

Hence proved.

:)

Answer 2

Step-by-step explanation:

Question:- If q is the mean proportion between p and r , Prove that

p² - q² + r² = q⁴(1/p² - 1/q² + 1/r²)

Solution:-

Since, q is the mean proportional of p and r.

Hence, q² = pr

L.H.S. = q⁴[1/p² – 1/q²2 + 1/r²]

= q⁴[1/p² – 1/pr + 1/r²]

= q⁴[r² – pr + p²/p²r²]

= q²[p² – pr + r²/(pr)²]

= q⁴[p² – pr + r²/q⁴]

= p² – pr + r² = R.H.S