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Algebra

Multiple Choice Questions

231.

If x + y + z = 6 and x² + y² + z² = 20, then the value of x³ + y³ + z³ - 3xyz is

38 Views

232.

If (x + y) = 1, then the value of
$fraction numerator 1 over denominator straight x cubed straight y cubed end fraction space minus space straight x cubed space minus space straight y cubed$ is

3
-3
1
-1

27 Views

233.

If a + b + c = 2s, then
$fraction numerator left parenthesis straight s minus straight a right parenthesis squared space plus space left parenthesis straight s minus straight b right parenthesis squared space plus space left parenthesis straight s minus straight c right parenthesis squared space plus space straight s squared over denominator straight a squared space plus space straight b squared space plus space straight c squared end fraction$ is equal to

a² + b² + c²
0
1
2

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234.

If $straight a space plus space fraction numerator 1 over denominator straight a minus 2 end fraction space equals space 4 comma$ then the value of

0
2
-2
4

27 Views

235.

If a³ - b³ - c³ = 0, then the value of a⁹ - b⁹ - c⁹ - 3a³b³c³ is

1
2
0
-1

26 Views

236.
If x = 332, y = 333, z = 335, then the value of x³ + y³ + z³ - 3xyz is

10000

7000

9000

8000

7000

$straight a cubed space plus space straight b cubed space plus space straight c cubed space minus space 3 abc space equals space 1 half open square brackets open parentheses straight a plus straight b plus straight c close parentheses open square brackets left parenthesis straight a minus straight b right parenthesis squared space plus space left parenthesis straight b minus straight c right parenthesis squared space plus space left parenthesis straight c minus straight a right parenthesis squared close square brackets space close square brackets$

$equals space 1 half open square brackets left parenthesis 332 space plus space 333 space plus space 335 right parenthesis space open square brackets left parenthesis 332 minus 333 right parenthesis squared space plus space left parenthesis 333 minus 335 right parenthesis squared space plus space left parenthesis 335 minus 332 right parenthesis squared close square brackets close square brackets equals space 1 half open square brackets 1000 space open square brackets left parenthesis negative 1 right parenthesis squared space plus space left parenthesis negative 2 right parenthesis squared space plus space left parenthesis 3 right parenthesis squared close square brackets close square brackets equals space 1 half open square brackets 1000 space cross times space 14 close square brackets equals space 7000$

237.

If m = -4, n = -2, then the value of
m³ - 3m² + 3m + 3n + 3n² + n³

-126
124
126
-124

238.

The value of $fraction numerator 1 over denominator square root of 7 minus square root of 6 end fraction space minus space fraction numerator 1 over denominator square root of 6 begin display style minus end style begin display style square root of 5 end style end fraction plus fraction numerator 1 over denominator square root of 5 begin display style minus end style begin display style 2 end style end fraction minus fraction numerator 1 over denominator square root of 8 begin display style minus end style begin display style square root of 7 end style end fraction plus fraction numerator 1 over denominator 3 minus square root of 8 end fraction$

239.

If $straight x space equals space fraction numerator 2 plus square root of 3 over denominator 2 minus square root of 3 end fraction space comma$ then the value of $straight x space plus space 1 over straight x ?$

14
$8 square root of 3$
0
18

240.

If $straight x space equals space 2 space plus space square root of 3 comma space$ then what is the value of $square root of 2 straight x space plus space fraction numerator 1 over denominator square root of 2 straight x end root end fraction ?$

$2 square root of 3$
$3 square root of 3$
$fraction numerator left parenthesis 3 square root of 3 space plus space 1 right parenthesis over denominator 2 end fraction$
$2 square root of 3 space plus space 1$