If a2 + b2 + c2 = 2(a – b – c) – 3 then what will be value of (2a – 3b + 4c) ?
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Solution
∵ a2 + b2 + c2 = 2(a – b – c) – 3⇒ a2 – 2a + 1 + b2 + 2b + 1 + c2 + 2c + 1 = 0
⇒ (a-1)2 + (b+1)2 + (c+1)2 = 0
⇒ a = 1, b = – 1, c = – 1
So,
2a – 3b + 4c = 2×1 – 3×(–1) + 4 (–1)
= 1
If x = 2 + , y = 2– then what will be value of ?
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Solution
x = 2 + y = 2 –
⇒ x + y = 4
& xy = 4 – 3 = 1
So अत: =
=
=
If = 98 (a > 0) then what will be value of ?
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Solution
a2 + = 98 ........(i)
⇒ a2 + = 98 + 2 = 100
⇒ ........(ii)
Multiplying,
= 98 × 10
= = 980
= = 980 – 10 ⇒ 970
If a + b +c = 10 and ab + bc + ca = 31 then what will be value of a2 + b2 + c2 ?
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Solution
a + b + c = 10
a2 + b2 + c2 + 2 (ab + bc + ca) = 100
⇒ a2 + b2 + c2 = 100 – (2 × 31)
= 38
If x = 12 and y = 4 then will be :-
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Solution
x = 12, y = 4
= = 3.
So = (16)3 = 4096.
If a + b + c = 0 then what will be value of ?
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Solution
a + b + c = 0 ⇒ (a + b + c)2 = 0
= a2 + b2 + c2 + 2 (ab + bc + ca) = 0
= a2 + b2 + c2 + 2 (c{a + b} + ab) = 0
= a2 + b2 + c2 + 2 (–c2 + ab) = 0
= a2 + b2 + c2 = 2 [c2 – ab]
Substituting =
If then what will be value of ?
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Solution
∵ x +
∴
=
=
= 3 × (32-3) = 18
What should be added to ‘7x3 – 5x2 + 3x – 10′ to make it divisible by (x – 1)?
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Solution
The term will be divisible by x – 1 if (x – 1) is a factor of given term = 7x3 – 5x2 + 3x – 10
put x = 1
= 7 – 5 + 3 – 10 = – 5.
to make it zero we should add '+ 5'.
What should be added to to make it :
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Solution
The required term will be.
=
If x + y = 3 and xy =2 , then what will be value of x3 – y3 ?
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Solution
x3 – y3 = (x – y) (x2 + y2 + xy)
x + y = 3 ------------(i)
xy = 2
(x – y)2 = (x + y)2 – 4xy = 9 – 8
x – y = 1 -----------(ii)
from equations (i) & (ii)
x = 2, y = 1
⇒ x3 – y3 = (2)3 – 13 = 7