Find the value of (2^(1/4)-1)(2^(3/4)+2^(1/2)+2^(1/4)+1)

Question

Find the value of \((2^{\frac14}-1)(2^{\frac34}+2^{\frac12}+2^{\frac14}+1)\)

(a) 2 

(b) 3 

(c) 5 

(d) 1

Answer 1

(d) 1

\(\bigg(2^{\frac14}-1\bigg)\bigg(2^{\frac34}+2^{\frac12}+2^{\frac14}+1\bigg)\)

Let \(2^{\frac14}\) = a . Then, 

Given exp. = (a – 1) (a³ + a² + a + 1 ) 

= (a – 1) (a² (a + 1) + 1(a + 1)) 

= (a – 1) (a + 1) (a² + 1) = (a² – 1) (a² + 1) 

= a⁴ – 1

∴ Required value = \(\big(2^{\frac14}\big)^4\) -1 = 2 - 1 = 1.