Elementary Algebra
- The degree f polynomial p(x) = x3 + 1 + 2x = 6x + 1/x is ?
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x3 + 1 + 2x =6x + 1/x
x3 + 1 + 2x = (6x2 + 1)/x
(x3 + 1 + 2x)x = 6x2 + 1
x4 - 4x2 - 6x2 -1 =0
x4 - 4x2 + x - 1 =0Correct Option: B
x3 + 1 + 2x =6x + 1/x
x3 + 1 + 2x = (6x2 + 1)/x
(x3 + 1 + 2x)x = 6x2 + 1
x4 - 4x2 - 6x2 -1 =0
x4 - 4x2 + x - 1 =0
Degree of polynomial is highest exponent degree term i.e.,4.
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If x = 2 + √3, then the value of √x + 1 is : √x
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As per given question,
x = 2 + √31 = 1 x 2 + √3 1 = 1 x 2 - √3 x 2 + √3 2 - √3 1 = 2 - √3 = 2 - √3 x 4 - 3 ( √x + 1 )2 = x + 1 + 2 = 2 + √3 + 2 - √3 + 2 . √x x
Correct Option: B
As per given question,
x = 2 + √31 = 1 x 2 + √3 1 = 1 x 2 - √3 x 2 + √3 2 - √3 1 = 2 - √3 = 2 - √3 x 4 - 3 ( √x + 1 )2 = x + 1 + 2 = 2 + √3 + 2 - √3 + 2 . √x x √x + 1 = √6 √x
- If a3 – b3 = 56 and a – b = 2, then the value of ( a2 + b2 ) is :
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As we know from the algebra formula,
(a – b)3 = a3 – b 3 – 3ab (a – b) .......................(1)
As per given question,
a3 – b 3 = 56 and a – b = 2
Put these value in above equation (1) . We will get,
⇒ 23 = 56 – 3ab x 2
⇒ 8 = 56 – 3ab x 2
⇒ 8 = 56 – 6ab
⇒ 6ab = 56 – 8 = 48
⇒ ab = 8 ...................... (i)Correct Option: C
As we know from the algebra formula,
(a – b)3 = a3 – b 3 – 3ab (a – b) .......................(1)
As per given question,
a3 – b 3 = 56 and a – b = 2
Put these value in above equation (1) . We will get,
⇒ 23 = 56 – 3ab x 2
⇒ 8 = 56 – 3ab x 2
⇒ 8 = 56 – 6ab
⇒ 6ab = 56 – 8 = 48
⇒ ab = 8 ...................... (i)
∴ a2 + b2 = (a – b)2 + 2ab
∴ a2 + b2 = (a – b)2 + 2ab
Put the value of
∴ a2 + b2 = 22 + 2 x 8
∴ a2 + b2 = 4 + 16 = 20
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If (5x2 – 3y2) : xy = 11 : 2, then the positive value of x is : y
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Given that :- 5x2 - 3y2 = 11 xy 2
10x2 – 6y2 = 11xy
10x2 – 11xy – 6y2 = 0
10x2 – 15xy + 4xy – 6y2 = 0Correct Option: C
Given that :- 5x2 - 3y2 = 11 2y 2
10x2 – 6y2 = 11xy
10x2 – 11xy – 6y2 = 0
10x2 – 15xy + 4xy – 6y2 = 0
5x (2x – 3y) + 2y (2x – 3y) = 0
(5x + 2y) (2x – 3y)
5x ≠ 2y, 2x = 3yx = 3 y 2
- If P = (0.08)2, Q = 1/(0.08)2 and R = (1 – 0.08)2 – 1, then out of the following the true relation is
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Given that in the question,
P = (0.08)2 = 0.0064Q = 1 = 10000 = 156.25 (0.08)2 64
R = (1 – 0.08)2 – 1
R = 1 + (0.08)2 – 2 × 0.08 – 1Correct Option: D
Given that in the question,
P = (0.08)2Q = 1 = 10000 = 156.25 (0.08)2 64
R = (1 – 0.08)2 – 1
R = 1 + (0.08)2 – 2 × 0.08 – 1 = (0.08)2 – 2 × 0.08
Clearly, R < P < Q
