Algebra
- For a > b, if a + b = 5 and ab = 6, then the value of (a2 – b2) is
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(a – b)2 = (a + b)2 – 4ab
= 52 – 4 × 6 = 1
⇒ a – b = 1
∴ (a2 – b2)
= (a + b) (a – b) = 5Correct Option: C
(a – b)2 = (a + b)2 – 4ab
= 52 – 4 × 6 = 1
⇒ a – b = 1
∴ (a2 – b2)
= (a + b) (a – b) = 5
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If x = 5 + 2√6, then the value of 
√x + 1 
is, √x
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x = 5 + 2√6
∴ 1 = 1 = 5 − 2√6 x 5 + 2√6 (5 + 2√6)(5 − 2√6) = 5 − 2√6 = 5 − 2√6 25 − 24 ∴ √x + 1 2 = x + 1 + 2 √x x
= 5 + 2√6 + 5 – 2√6 + 2 = 12∴ √x + 1 = √12 = 2√3 √x Correct Option: C
x = 5 + 2√6
∴ 1 = 1 = 5 − 2√6 x 5 + 2√6 (5 + 2√6)(5 − 2√6) = 5 − 2√6 = 5 − 2√6 25 − 24 ∴ √x + 1 2 = x + 1 + 2 √x x
= 5 + 2√6 + 5 – 2√6 + 2 = 12∴ √x + 1 = √12 = 2√3 √x
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If x − 1 = 4 , then x + 1 is equal to x x
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x − 1 = 4 (Given) x ∴ x + 1 2 = x − 1 2 + 4 x x
= (4)2 + 4 = 20⇒ x + 1 = √20 = 2√5 x Correct Option: B
x − 1 = 4 (Given) x ∴ x + 1 2 = x − 1 2 + 4 x x
= (4)2 + 4 = 20⇒ x + 1 = √20 = 2√5 x
- If √x = √3 − √5 , then the value of x2 – 16x + 6 is
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√x = √3 - √5
On squaring both sides,
x = 3 + 5 - 2√15
⇒ x - 8 = - 2√15
Squaring again,
x² – 16x + 64 = 60
⇒ x² – 16x + 4 = 0
∴ x² – 16x + 6 = 2Correct Option: C
√x = √3 - √5
On squaring both sides,
x = 3 + 5 - 2√15
⇒ x - 8 = - 2√15
Squaring again,
x² – 16x + 64 = 60
⇒ x² – 16x + 4 = 0
∴ x² – 16x + 6 = 2
- The minimum value of (x – 2) (x – 9) is
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Expression = (x – 2) (x – 9)
= x² – 11x + 18 = ax² + bx + cMinimum value = 4ac - b² 4a = 4 × 1 × 18 - 121 = - 49 4 4 Correct Option: D
Expression = (x – 2) (x – 9)
= x² – 11x + 18 = ax² + bx + cMinimum value = 4ac - b² 4a = 4 × 1 × 18 - 121 = - 49 4 4
