If x = 2 + 223 + 213 then find the value of x3-6x2+6x ? 1 2 3 4 Given that x = 2

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Question
If x = 2 + 223 + 213 then find the value of x3-6x2+6x ?
Options
A. 1
B. 2
C. 3
D. 4

Correct Answer

2

Explanation

Given that $x = 2 + 2^{\frac{2}{3}} + 2^{\frac{1}{3}}$

So x - 2 = $2^{\frac{2}{3}} + 2^{\frac{1}{3}}$

Now cubing on both sides, we get

=> $x^{3} - 8 - 6 x^{2} + 12 x = 4 + 2 + 6 (x - 2)$

Therefore, $x^{3} - 6 x^{2} + 6 x = - 6 + 8 = 2$

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Square Root and Cube Root problems

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1. If 3a=4b=6c and a+b+c=2729 , then a2+b2+c2 =?
Options
A. 81
B. 83
C. 87
D. None of these

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Correct Answer: 87

Explanation:

$4 b = 6 c ? b = \frac{3}{2} c a n d 3 a = 4 b ? a = \frac{4}{3} b = \frac{4}{3} (\frac{3}{2} c) = 2 c$

$a + b + c = 27 \sqrt{29} ? 2 c + \frac{3}{2} c + c = 27 \sqrt{29} ? c = 6 \sqrt{29}$

$? \sqrt{a^{2} + b^{2} + c^{2}} = \sqrt{(a + b + b)^{2} - 2 (a b + b c + c a)}$

$= \sqrt{(27 \sqrt{29})^{2} - 2 (2 c � \frac{3}{2} c + \frac{3}{2} c � c + c � 2 c)}$

$= \sqrt{(729 � 29) - 2 � \frac{13}{2} c^{2}}$

= 87

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4. If 35+125=17.88 , then what will be the value of 80+65 =?
Options
A. 13.41
B. 20.46
C. 21.66
D. 22.35

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8. If x�y = x + y + xy , the value of 6x24 is:
Options
A. 41
B. 42
C. 43
D. 44

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If x = 2 + 223 + 213 then find the value of x3-6x2+6x ?

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If x = 2 + 223 + 213 then find the value of x3-6x2+6x ?

Square Root and Cube Root problems

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