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231.
If x + y + z = 6 and x² + y² + z² = 20, then the value of x³ + y³ + z³ - 3xyz is

64

70

72

76

x + y + z = 6
S.B.S.
(x + y + z)² = x² + y² + z² + 2(xy + yz + zx)
⟹ (6)² = 20 + 2(xy + yz + zx)
⟹ 36 = 20 + 2(xy + yz + zx)
⟹ 36 - 20 = 2(xy + yz + zx)
⟹ 16 = 2(xy + yz + zx)
⟹ (xy + yz + zx) = 8
∴ x³ + y³ + z³ - 3xyz
= (x + y + z) (x² + y² + z² - (xy + yz + zx)
= 6 (20 - 8) = 6 x 12 = 72

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

29 Views

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

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 $square root of 2 straight x space plus space fraction numerator 1 over denominator square root of 2 straight x end root end fraction ?$

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