himu wrote:How many roots does this equation have?
sqrt(x^2 + 1) + sqrt(x^2 + 2) = 2
0
1
2
3
4
Every test-taker should know that √2≈1.4.
Since the square of a value cannot be negative, the least possible value of x² is 0.
Substituting x²=0 into √(x²+1) + √(x²+2) = 2, we get:
√(0²+1) + √(0²+2) = 2
√1 + √2 = 2.
2.4 = 2.
Doesn't work:
The lefthand side is greater than the righthand side.
Since there is no way to decrease the value of the lefthand side, the equation has no solutions.
The correct answer is
A.
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