An algebra problem by Ritik Devnani

Algebra Level 2

If P P and Q Q are 2 numbers such that P Q = 10 PQ=10 and P 2 Q + P Q 2 + P + Q = 99 P^{2}Q + PQ^{2} + P + Q = 99 then find P 2 + Q 2 P^{2} + Q^{2} .

61 51 55 65

Ritik Devnani by Ritik Devnani , 17, India

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1 solution

Substitute PQ = 10 into the equation gives: 10P + 10Q + P + Q = 99. This leads to P + Q = 9, so:

( P + Q ) 2 = P 2 + Q 2 + 2 P Q = 81 → P 2 + Q 2 = 61 (P+Q) ^2 = P^2 + Q^2 + 2PQ = 81 \rightarrow P^2 + Q^2 = 61 .

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Thank you Peter Van der Linden.

Ritik Devnani - 3 years, 8 months ago

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