Question : If $m - n = 2$ and $m n = 15, (m, n > 0)$ , then the value of $(m^{2} - n^{2}) (m^{3} - n^{3})$ is:
Option 1: 1856
Option 2: 1658
Option 3: 1586
Option 4: 1568

Question

Question : If $m = \sqrt{5 + \sqrt{5 + \sqrt{5 + . . . . . . . .}}}$ and $n = \sqrt{5 - \sqrt{5 - \sqrt{5. . . . . . . . . . .}}}$ then among the following, the relation between m and n is:

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Answer 1

Correct Answer: 1568

Solution : Given:
$m - n = 2$ and $m n = 15, (m, n > 0)$
$(m - n)^{2} = 2^{2}$
⇒ $m^{2} + n^{2} - 2 m n = 4$
⇒ $m^{2} + n^{2} = 4 + (2 \times 15) = 34$
⇒ $m^{2} + n^{2} + 30 = 34 + 30$ [adding 30 to both sides]
⇒ $m^{2} + n^{2} + 2 m n = 64$ [as, $m n = 15$ ]
⇒ $(m + n)^{2} = 8^{2}$
⇒ $m + n = 8$
Now, $(m^{2} - n^{2}) (m^{3} - n^{3})$
= $(m + n) (m - n) (m - n) (m^{2} + m n + n^{2})$
= $8 \times 2 \times 2 \times (34 + 15)$
= $1568$
Hence, the correct answer is 1568.

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Question : If m−n=2 and mn=15,(m,n>0) , then the value of (m2−n2)(m3−n3) is:Option 1: 1856Option 2: 1658Option 3: 1586Option 4: 1568

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Question : If $m - n = 2$ and $m n = 15, (m, n > 0)$ , then the value of $(m^{2} - n^{2}) (m^{3} - n^{3})$ is:
Option 1: 1856
Option 2: 1658
Option 3: 1586
Option 4: 1568