How many roots does the equation \(\sqrt{x^2+1}+\sqrt{x^2+2}=2\) have?
A. 0
B. 1
C. 2
D. 3
E. 4
Answer: A
Source: GMAT Club Tests
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How many roots does the equation \(\sqrt{x^2+1}+\sqrt{x^2+2}=2\) have?
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regor60
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The X^2 inside the radicals means the left side is always increasing with increasing X and symmetrical around the Y axis, which also means that the left side -2 is always increasing.
If the Y intercept is 0 or greater, then the curve doesn't intercept the X axis since the curve would be entirely above Y=0.
The Y intercept is found by setting X=0:
1+2^(1/2)-2 is about 1+1.4-2, which means a positive Y intercept so the answer is 0,A
If the Y intercept is 0 or greater, then the curve doesn't intercept the X axis since the curve would be entirely above Y=0.
The Y intercept is found by setting X=0:
1+2^(1/2)-2 is about 1+1.4-2, which means a positive Y intercept so the answer is 0,A
