Question 2

# Calculate the value of $$(5^\frac{1}{4}-1)(5^\frac{3}{4}+5^\frac{1}{2}+5^\frac{1}{4}+1)$$

Solution

Expression = $$(5^\frac{1}{4}-1)(5^\frac{3}{4}+5^\frac{1}{2}+5^\frac{1}{4}+1)$$

= $$(5^\frac{1}{4}-1)[(5^\frac{1}{4})^3+(5^\frac{1}{4})^2+(5^\frac{1}{4})+1]$$

Let $$5^{\frac{1}{4}}=x$$

= $$(x-1)(x^3+x^2+x+1)$$

= $$(x^4-1)$$

= $$(5^{\frac{1}{4}})^4-1$$

= $$5-1=4$$

=> Ans - (B)