If p + q = 10, and pq = 5, then find the numeric value of :-
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Solution
=
If x = , then find the value of .
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Solution
∵
Square both sides,
⇒
∴
=
If , then what is the value of ?
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Solution
∵
⇒ x2 + a = x
⇒ x2 – x + a = 0 ⇒ x2 – x = – a
So,
⇒
If , then find the value of :-
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Solution
∵ or,
⇒
⇒
Similarly =
So,
=
=
=
=
If where a ≠0, b ≠ 0 then a3 +b3 = ?
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Solution
= a2 + b2 = ab
= a2 + b2 – ab = 0
Now a3 + b3 = (a + b) (a2 + b2 – ab)
a3 + b3 = (a + b) (0) = 0
If x2 = y + z, y2 = z + x, z2 = x + y then will be.
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Solution
x2 = y +z
= x2 + x = x + y + z
= x(x + 1) = x + y + z
= (x + 1) =
=
Similarly
So
=
If x2 + y2 + then x2 + y2 = ?
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Solution
x2 + y2 + = 4
⇒ = 0
⇒
So (x2 – 1)2 = 0
and (y2 – 1)2 = 0
So x2 + y2 = 1 + 1 = 2
If , then what will be value of x18 + x12 + x6 + 1 ?
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Solution
∵ x +
Cubing both sides
=
⇒
⇒ x6 + 1 = 0
⇒ x6 = – 1
So,
x18 + x12 + x6 + 1
= (x6)3 + (x6)2 + x6 + 1
= (–1)3 + (–1)2 + (–1) + 1 = 0
If a = 2.361, b = 3.263 and c = 5.624 then value of “a3 + b3 – c3 + 3abc” is?
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Solution
Given, a = 2.361, b = 3.263, c = 5.624
∵ a+b = c
Cubing both sides
(a + b)3 = c3
⇒ a3 + b3 + 3ab (a + b) = c3
⇒ a3 + b3 – c3 + 3abc = 0
If a2 = b + c, b2 = c + a and c2 = a + b then will be equal to ?
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Solution
a2 = b + c
⇒ a = ⇒ a + 1 =
Similarly,
∵
=
=