Question

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. 534/255
2. 17/15
3. 514/225
4. 514/255

Answer 1

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.