Algebra
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If 
x + 1 
= 5, then the value of 5x is : x x2 + 5x + 1
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It is given, x + 1 = 5 x Expression =
5x x2 + 5x + 1 = 5x x x + 5 + 1 x = 5 x + 1 + 5 x = 5 = 5 = 1 5 + 5 10 2 Correct Option: C
It is given, x + 1 = 5 x Expression =
5x x2 + 5x + 1 = 5x x x + 5 + 1 x = 5 x + 1 + 5 x = 5 = 5 = 1 5 + 5 10 2
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If 2 + a + 2 + b + 2 + c = 4, then the value of ab + bc + ca is a b c abc
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2 + a + 2 + b + 2 + c = 4 a b c ⇒ 2 + 1 + 2 + 1 + 2 + 1 = 4 a b c ⇒ 2 + 2 + 2 = 4 – 3 = 1 a b c ⇒ 1 + 1 + 1 = 1 a b c 2 ⇒ bc + ca + ab = 1 abc 2 Correct Option: D
2 + a + 2 + b + 2 + c = 4 a b c ⇒ 2 + 1 + 2 + 1 + 2 + 1 = 4 a b c ⇒ 2 + 2 + 2 = 4 – 3 = 1 a b c ⇒ 1 + 1 + 1 = 1 a b c 2 ⇒ bc + ca + ab = 1 abc 2
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If x2 – 3x + 1 = 0, (x ≠ 0), then the value of x + 1 is x
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x2 – 3x + 1 = 0
⇒ x2 + 1 = 3x
On dividing by x,x2 + 1 = 3x x x ⇒ x + 1 = 3 x Correct Option: C
x2 – 3x + 1 = 0
⇒ x2 + 1 = 3x
On dividing by x,x2 + 1 = 3x x x ⇒ x + 1 = 3 x
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If x + 1 = 6, then value of x2 + 1 is : x x²
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x + 1 = 6 x
On squaring both sides,x + 1 2 = 36 x ⇒ x2 + 1 + 2 = 36 x2 ⇒ x2 + 1 = 36 – 2 = 34 x2 Correct Option: C
x + 1 = 6 x
On squaring both sides,x + 1 2 = 36 x ⇒ x2 + 1 + 2 = 36 x2 ⇒ x2 + 1 = 36 – 2 = 34 x2
- If a (x + y) = b(x – y) = 2ab, then the value of 2 (x2 + y2) is :
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a (x + y) = b (x – y)
⇒ ax – bx = – by – ay
⇒ bx – ax = ay + by
⇒ x (b – a) = y (a + b)⇒ x = y a + b b − a = x2 + y2 = x2 + y2 (a + b)2(b − a)2 2(a2 + b2)
∴ 2(x2 + y2) = 4(a2 + b2)Correct Option: D
a (x + y) = b (x – y)
⇒ ax – bx = – by – ay
⇒ bx – ax = ay + by
⇒ x (b – a) = y (a + b)⇒ x = y a + b b − a = x2 + y2 = x2 + y2 (a + b)2(b − a)2 2(a2 + b2)
∴ 2(x2 + y2) = 4(a2 + b2)
