How do I compare?

Algebra Level 2

x = 11 + 5 y = 10 + 6 z = 3 + 13 x=\sqrt{11}+\sqrt{5} \\ y=\sqrt{10}+\sqrt{6} \\ z=\sqrt{3}+\sqrt{13}

For x x , y y and z z as given above, which of the following is true?

y > z > x y>z>x y > x > z y>x>z x > y > z x>y>z x > z > y x>z>y

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2 solutions

Ankur Sharma
Oct 3, 2016

squre on both side and compare

Or look at the graph of y = x y=\sqrt x

Arulx Z - 4 years, 8 months ago

x 2 = 16 + 2 55 { x }^{ 2} = 16+2\sqrt {55 }
y 2 = 16 + 2 60 { y }^{ 2} = 16+2\sqrt {60 }
z 2 = 16 + 2 39 { z }^{ 2} = 16+2\sqrt {39 }

SO

60 > 55 > 39 \sqrt { 60 } >\sqrt { 55 } >\sqrt { 39 }

THEN

y > x > z y>x>z

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