# Algebra

12
 Question 1
If x3 + y3 = 9 and x + y = 3, then the value of x4+y4 is,
 A 21 B 0 C 17 D 25
Algebra
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Question 1 Explanation:
```x3+y3 = (x + y) × (x2 − xy + y2)

Putting given values of x3+y3 and (x + y)
9 = 3 × ((x+y)2 − 3xy)
= 3 × (9 − 3xy)
= 27 − 9xy

9xy = 18
xy = 2

x4 + y4 = (x2 + y2)2 - 2x2y2
= (x2 + y2)2 - 2*4
[Putting value of xy]
= ((x + y)2 - 2xy)2 - 2*4
[Putting values of (x+y) and xy]
= (9 - 4)2 - 2*4
= 17```
 Question 2
If x+1/2x = 2, find the value of 8x3+1/x3
 A 40 B 20 C 28 D 35
Algebra
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 Question 3
For any real number x the maximum value of 4−6x−x2 is at x=,
 A 4 B 6 C -3 D 3
Algebra
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Question 3 Explanation:
Differentiate and equate to 0 6+2x =0 x=−3
 Question 4
If 5√x +12√x =13√x then value of x is,
 A 2 B 1 C 3 D 4
Algebra
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Question 4 Explanation:
say x=1
17!=13

for, x=2 and 3 also not possible
x=4
52+122=132
169=169
 Question 5
 A 0 B -2 C 2 D 4
Algebra
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Question 5 Explanation:
 Question 6
 A 0 B 6 C -4 D 4
Algebra
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Question 6 Explanation:
 Question 7
 A 8 B 2 C 0 D 6
Algebra
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Question 7 Explanation:
 Question 8
 A 7/4 B 9/4 C 5/4 D 3/4
Algebra
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Question 8 Explanation:
 Question 9
 A 6 B 2 C 3 D 0
Algebra
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Question 9 Explanation:
Put -ac = ab + bc ; -ab = ac+ bc and -bc =ab + ac
(ab + bc + ca)/[(a+b+c)(abc)]
as, ab+bc+ca=0
= 0
 Question 10