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Algebra

Multiple Choice Questions

241.

If $straight x space plus space 1 over straight x space equals space 4 comma space$ then what is the value of $straight x to the power of 6 space plus space 1 over straight x to the power of 6 ?$

52
256
1026
2702

242.

If $straight y space equals space fraction numerator 2 minus straight x over denominator 1 plus straight x end fraction comma$ then what is the value of $fraction numerator 1 over denominator straight y space plus space 1 end fraction space plus space fraction numerator 2 straight y space plus space 1 over denominator straight y squared minus 1 end fraction ?$

$fraction numerator left parenthesis 1 space plus space straight x right parenthesis thin space left parenthesis 2 space minus space straight x right parenthesis over denominator 2 straight x minus 1 end fraction$
$fraction numerator left parenthesis 1 space minus space straight x right parenthesis thin space left parenthesis 2 space plus space straight x right parenthesis over denominator straight x space minus space 1 end fraction$
$fraction numerator left parenthesis 1 space plus space straight x right parenthesis thin space left parenthesis 2 space minus space straight x right parenthesis over denominator 1 space minus space 2 straight x end fraction$
$fraction numerator left parenthesis 1 plus straight x right parenthesis thin space left parenthesis 1 minus 2 straight x right parenthesis over denominator 2 minus straight x end fraction$

243.
If a³ + b³ = 35 and ab = 6, then what is the value of a + b?

5

8

2

-8

Let a + b = x
C.B.S.
(a + b)³ = a³ + b³ + 3ab(a + b)
⟹ x³ = 35 + 3 x 6 x (x)
⟹ x³ - 18x = 35
⟹ x(x² - 18) = 5 x 7
check with the option,
Now,
⟹ x = 5, x² -18 = 7
∴ a + b = 5