If p + q = 4 and p2 + q2 = 10, find p4 + q4 - 2p2q2.
64
Note that \(p^4 + q^4 - 2p^2q^2 = (p^2 - q^2)^2 = \left[(p+q)(p-q)\right]^2\).
From \((p+q)^2 = p^2+q^2+2pq\): \(16 = 10 + 2pq \Rightarrow pq = 3\).
Also \((p-q)^2 = p^2+q^2-2pq = 10 - 6 = 4\), so \((p-q)^2 = 4\).
Thus \((p^2-q^2)^2 = (p+q)^2(p-q)^2 = 16\times4 = 64\).
The value of p4 + q4 - 2p2q2 is 64.
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Important Questions from Identities
If x 2 + 4y 2 = 40, xy = 6 and x > 2y then the value of x - 2y is:
- \(\dfrac{(5.17-2.19)^2-(5.17+2.19)^2}{11.3223}\)
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If a + b + c = 5, a 2+ b 2+ c 2= 27, a 3 + b 3 + c 3 = 125, then the value of \(\frac{abc}{5}\) is:
(999) 2- 2 2=
