compare-without-calculator-5-1-7-1-and-7-1-5-1-

Question Number 135378 by Bird last updated on 12/Mar/21

c o m p a r e w i t h o u t c a l c u l a t o r

5 (\sqrt{1 + \sqrt{7}} - 1) a n d 7 (\sqrt{1 + \sqrt{5}} - 1)

Answered by mr W last updated on 12/Mar/21

5 (\sqrt{1 + \sqrt{7}} - 1) < 5 (\sqrt{1 + \sqrt{9}} - 1) = 5

7 (\sqrt{1 + \sqrt{5}} - 1) > 7 (\sqrt{1 + \sqrt{4}} - 1) = 7 (\sqrt{3} - 1)

= 7 \sqrt{3} - 7 = 7 \sqrt{\frac{147}{49}} - 7 > 7 \sqrt{\frac{144}{49}} - 7

= 7 \times \frac{12}{7} - 7 = 12 - 7 = 5

s i n c e 7 (\sqrt{1 + \sqrt{5}} - 1) > 5 a n d

5 (\sqrt{1 + \sqrt{7}} - 1) < 5,

\Rightarrow 7 (\sqrt{1 + \sqrt{5}} - 1) > 5 (\sqrt{1 + \sqrt{7}} - 1)

Commented by mathmax by abdo last updated on 12/Mar/21

thankx sir mrw