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Q.1. If p(x) = x^{2} – 2√2 x + 1, then find p (2√2) .
Sol. Since, p(x) = x^{2 }– 2 √2 x + 1
= 4 (2) – 4 (2) + 1 = 8 – 8 + 1 = 1
Q.2. If a + b + c = 9, and ab + bc + ca = 26, find a^{2 }+ b^{2} + c^{2}
Sol. (a + b + c)^{2} = (a^{2 }+ b^{2 }+ c^{2}) + 2 (ab + bc + ca)
⇒ (9)^{2 }= (a^{2} + b^{2 }+ c^{2}) + 2 (26) = (a^{2 }+ b^{2} + c^{2}) + 52
⇒ a^{2} + b^{2 }+ c^{2} =9^{2}– 52 = 81– 52 = 29
Q.3. Factorise :
Sol.
Q.4. If a, b, c are all nonzero and a + b + c = 0, prove that
Sol. ∵ a + b + c = 0 ⇒ a^{3} + b^{3} + c^{3} – 3abc = 0
or a^{3 }+ b^{3 }+ c^{3} = 3abc ⇒
Q.5. Prove that (a + b + c)^{3} – a^{3} – b^{3} – c^{3} = 3(a + b) (b + c) (c + a)
Sol.
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