Question : If $x = \sqrt[3]{28}, y = \sqrt[3]{27}$ , then the value of $x + y - \frac{1}{x^{2} + x y + y^{2}}$ is:
Option 1: 8
Option 2: 7
Option 3: 6
Option 4: 5

Question

Question : If $x = \frac{\sqrt{5} + 1}{\sqrt{5} - 1}$ and $y = \frac{\sqrt{5} - 1}{\sqrt{5} + 1}$ , then the value of $\frac{x^{2} + x y + y^{2}}{x^{2} - x y + y^{2}}$ is:

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Answer 1

Correct Answer: 6

Solution : Given: $x = \sqrt[3]{28}$ and $y = \sqrt[3]{27} .$
To find $x + y - \frac{1}{x^{2} + x y + y^{2}}$
Multiplying and dividing by $(x - y)$
$= x + y - \frac{(x - y)}{(x - y) (x^{2} + x y + y^{2})}$
$= x + y - \frac{(x - y)}{(x^{3} - y^{3})}$
$= x + y - \frac{(x - y)}{(28 - 27)}$
$= x + y - x + y$
$= 2 y$
$= 2 \times \sqrt[3]{27}$
$= 2 \times 3 = 6$
Thus, $x + y - \frac{1}{x^{2} + x y + y^{2}} = 6$
Hence, the correct answer is 6.

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Question : If x=283,y=273, then the value of x+y−1x2+xy+y2 is:Option 1: 8Option 2: 7Option 3: 6Option 4: 5

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Question : If $x = \sqrt[3]{28}, y = \sqrt[3]{27}$ , then the value of $x + y - \frac{1}{x^{2} + x y + y^{2}}$ is:
Option 1: 8
Option 2: 7
Option 3: 6
Option 4: 5