# Find The Value ? If

If (X^{24} + 1)/ X^{12} = 7 then the value of (X^{72} + 1)/ X^{36} is :

- 433
- 322
- 343
- 432

**Answer: (2) 322**

**Explanation:-**

(x^{24} + 1)/x^{12} = 7

x^{24}/x^{12} + 1/ x^{12} = 7

x^{12} + 1/x^{12} = 7 ……………. (1)

Cube on both sides,

(x^{12} + 1/ x^{12})^{3} = 7^{3}

(x^{12})^{3 }+ (1/x^{12})^{3} + 3 (x^{12} + 1/x^{12}) = 7^{3}

x^{36} + 1/x^{36} + 3 x 7 = 343 (from equation 1)

x^{36} + 1/x^{36} = 343 – 21

x^{36} + 1/x^{36} = 322

Hence, the answer is (2) 322.