Question

compare a=√15+√11 , b=√14+√12 (Hint compare a^2 and b^2)​

Answer 1

Answer:

Step-by-step explanation:

a²=15+11+2√165 , b²=14+12+2√168

a²=26+2√165 , b²=26 + 2√168

a²=b²-2√168+2√165=b²

Answer 2

Answer:

B > A i.e $\sqrt{15} +\sqrt{11}$ < $\sqrt{14} + \sqrt{12}$

Step-by-step explanation:

$a^{2} = 15+ 11 + 2\sqrt{15* 11}$

$b^{2} = 14+ 12 + 2\sqrt{14*12}$

as 15+11 = 14+12 , we can check $\sqrt{14*12} and \sqrt{15*11}$

I.e $\sqrt{14*12} = \sqrt{168} \\and\\ \sqrt{15*11} = \sqrt{165}$

$\sqrt{168} > \sqrt{165}\\So, B > A.$