Question
Download Solution PDFIf \(\frac{\left(17\right) ^{3}+\left( 7\right) ^{3}}{(17^{2}+7^{2}-k)} =24, \)then what is the value of k?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
\(\frac{\left(17\right) ^{3}+\left( 7\right) ^{3}}{(17^{2}+7^{2}-k)} =24\)
Concept used:
a3 + b3 = (a + b)(a2 + b2 - ab)
Calculation:
\(\frac{\left(17\right) ^{3}+\left( 7\right) ^{3}}{(17^{2}+7^{2}-k)} =24\)
⇒ \(\frac{(17+7)(17^{2}+7^{2}-7\times17)}{(17^{2}+7^{2}-k)} =24\)
⇒ \(\frac{(17^{2}+7^{2}-119)}{(17^{2}+7^{2}-k)} =1\)
⇒ 172 + 72 - 119 = 172 + 72 - k
⇒ k = 119
∴ The value of k is 119.
Last updated on Jun 13, 2025
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