Algebra
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If 4x − 3 + 4y − 3 + 4z − 3 = 0, then the value of 1 + 1 + 1 is x y z x y z
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4x − 3 + 4y − 3 + 4z − 3 = 0 x y z ⇒ 4x − 3 + 4y − 3 + 4z − 3 = 0 x x y y z z ⇒ 3 + 3 + 3 = 4 + 4 + 4 = 12 x y z ⇒ 1 + 1 + 1 = 12 = 4 x y z 3 Correct Option: C
4x − 3 + 4y − 3 + 4z − 3 = 0 x y z ⇒ 4x − 3 + 4y − 3 + 4z − 3 = 0 x x y y z z ⇒ 3 + 3 + 3 = 4 + 4 + 4 = 12 x y z ⇒ 1 + 1 + 1 = 12 = 4 x y z 3
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If x + 1 = 99, find the value of 100x x 2x2 + 102x + 2
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x + 1 = 99 x ∴ 100x 2x2 + 102x + 2 = 100x 2x2 + 2 + 102x
On dividing by x,= 100 2x + 2 + 102 x = 100 2 
x + 1 
+ 102 x = 100 = 100 = 1 2 × 99 + 102 300 3 Correct Option: C
x + 1 = 99 x ∴ 100x 2x2 + 102x + 2 = 100x 2x2 + 2 + 102x
On dividing by x,= 100 2x + 2 + 102 x = 100 2 x + 1 + 102 x = 100 = 100 = 1 2 × 99 + 102 300 3
- If x – y = 2 and x2 + y2 = 20, then value of (x + y)2 is
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(x – y)2 = x2 + y2 – 2xy
⇒ 22 = 20 – 2xy
⇒ 2xy = 20 – 4 = 16
∴ (x + y)2 = x2 + y2 + 2xy
= 20 + 16 = 36Correct Option: B
(x – y)2 = x2 + y2 – 2xy
⇒ 22 = 20 – 2xy
⇒ 2xy = 20 – 4 = 16
∴ (x + y)2 = x2 + y2 + 2xy
= 20 + 16 = 36
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If a = 2 + √3, then the value of 
a2 + 1 
is : a2
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a = 2 + √3
1 = 1 a 2 + √3 = 1 × 2 − √3 2 + √3 2 − √3 = 2 − √3 = 2 − √3 4 − 3 ∴ a2 + 1 = a + 1 2 − 2 a2 a
= (2 + √3 + 2 − √3)2 − 2
= 16 – 2 = 14Correct Option: B
a = 2 + √3
1 = 1 a 2 + √3 = 1 × 2 − √3 2 + √3 2 − √3 = 2 − √3 = 2 − √3 4 − 3 ∴ a2 + 1 = a + 1 2 − 2 a2 a
= (2 + √3 + 2 − √3)2 − 2
= 16 – 2 = 14
- The term to be added to 121a2 +64b to make a perfect square is
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121a2 + 64b2
= (11a)2 + (8b)2
∵ (x + y)2 = x2 + y2 + 2xy
∴ Required expression
= 2 × 11a × 8b = 176abCorrect Option: A
121a2 + 64b2
= (11a)2 + (8b)2
∵ (x + y)2 = x2 + y2 + 2xy
∴ Required expression
= 2 × 11a × 8b = 176ab
