If x�y = x + y + xy , the value of 6x24 is: 41 42 43 44 G i v e n x � y = x + y

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

Correct Answer

42

Explanation

$G i v e n x � y = x + y + \sqrt{x y} H e r e x = 6, y = 24 T h e n, x � y = 6 + 24 + \sqrt{6 x 24} 6 x 24 = 30 + \sqrt{144} = 30 + 12 = 42 .$

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Square Root and Cube Root problems

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

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

Discuss

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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Correct Answer: 2

Explanation:

$\sqrt{(\frac{(0.75)^{3}}{1 - 0.75} + [0.75 + (0.75)^{2} + 1])} = \sqrt{\frac{(0.75)^{3} + (1 - 0.75) [(1)^{2} + (0.75)^{2} + 1 � 0.75]}{1 - 0.75}}$

= $\sqrt{\frac{(0.75)^{3} + [(1)^{3} - (0.75)^{3}]}{1 - 0.75}} = \sqrt{\frac{1}{0.25}} = \sqrt{4} = 2$

Discuss

Correct Answer: 5sqrt{3}

Explanation:

Given Exp = $\frac{3 \sqrt{2}}{\sqrt{6} - \sqrt{3}} � \frac{\sqrt{6} + \sqrt{3}}{\sqrt{6} + \sqrt{3}} - \frac{4 \sqrt{3}}{\sqrt{6} - \sqrt{2}} � \frac{\sqrt{6} + \sqrt{2}}{\sqrt{6} + \sqrt{2}} - \frac{6}{2 (\sqrt{2} - \sqrt{3})}$

= $\frac{3 \sqrt{2} (\sqrt{6} + \sqrt{3})}{6 - 3} - \frac{4 \sqrt{3} (\sqrt{6} + \sqrt{2})}{6 - 2} + \frac{3}{(\sqrt{3} - \sqrt{2})} � \frac{(\sqrt{3} + \sqrt{2})}{(\sqrt{3} + \sqrt{2})}$

= $\sqrt{2} (\sqrt{6} + \sqrt{3}) - \sqrt{3} (\sqrt{6} + \sqrt{2}) + 3 (\sqrt{3} + \sqrt{2})$

= $\sqrt{12} + \sqrt{6} - \sqrt{18} - \sqrt{6} + 3 \sqrt{3} + 3 \sqrt{2}$

= $5 \sqrt{3}$

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If x�y = x + y + xy , the value of 6x24 is:

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If x�y = x + y + xy , the value of 6x24 is:

Square Root and Cube Root problems

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