1.

Evaluate: \(\frac{17}{15} \times \frac{17}{15} \times \frac{17}{15}\space +\space \frac{15}{17} \times \frac{15}{17} \times \frac{15}{17} \over \frac{17}{15} \times \frac{17}{15}\space -\space 1 \space+\space \frac{15}{17} \times \frac{15}{17} \)1. 534/2552. 17/153. 514/2254. 514/255

Answer» Correct Answer - Option 4 : 514/255

Concept used:
a3 + b3 = (a + b) × (a2 – ab + b2)

Calculation:
\(\frac{17}{15} × \frac{17}{15} × \frac{17}{15}\space +\space \frac{15}{17} × \frac{15}{17} × \frac{15}{17} \over \frac{17}{15} × \frac{17}{15}\space -\space 1 \space+\space \frac{15}{17} × \frac{15}{17} \)
Let 17/15 and 15/17 be a and b respectively.
⇒ a × b = 17/15 × 15/17 = 1
⇒ (a × a × a + b × b × b)/(a × a – 1 + b × b)
⇒ (a3 + b3)/(a2 – ab + b2)
⇒ [(a + b) × (a2 – ab + b2)]/(a2 – ab + b2)
⇒ a + b
Putting the value of a and b,
⇒ 17/15 + 15/17
⇒ (17 × 17 + 15 × 15)/(15 × 17)
⇒ (289 + 225)/255
⇒ 514/255
∴ The correct answer is 514/255.


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