Solveeit Logo
Login

Question

Question: If \(\frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} + \sqrt{2}} = 1\) then \(2x + 3 = a(x - 3) + b(x + 1)\)...

If 3+23+2=1\frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} + \sqrt{2}} = 1 then 2x+3=a(x−3)+b(x+1)2x + 3 = a(x - 3) + b(x + 1)

A

x=3x = 3

B

2(3)+3=b(3+1)2(3) + 3 = b(3 + 1)

C

9=4b9 = 4b

D

None of these

Answer

9=4b9 = 4b

Explanation

Solution

125+255=5(12+211)\sqrt{12\sqrt{5} + 2\sqrt{55}} = \sqrt{\sqrt{5}(12 + 2\sqrt{11})}

=51/411+1+211=51/4(11+1)= 5^{1/4}\sqrt{11 + 1 + 2\sqrt{11}} = 5^{1/4}(\sqrt{11} + 1)

x=(93+112)1/3x = (9\sqrt{3} + 11\sqrt{2})^{1/3}.