If x= 34 and y= 25, what is the value of x^2 +6x +9- y^2 -2y +1?

If x= 34 and y= 25, what is the value of x^2… | GMAT Sprint

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PS · Problem Solving

705-805

Roots

If $x=\frac{3}{4}$ and $y=\frac{2}{5}$ , what is the value of $\sqrt{x^2 +6x +9}-\sqrt{y^2 -2y +1}$ ?

Answer Choices

Correct answer marked below

87/20

63/20

Correct

47/20

15/4

14/5

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Explanation

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Official Explanation

Official

Note that

\sqrt{x^2}=|x|

\sqrt{x^2 +6x +9}-\sqrt{y^2 -2y +1}=

= \sqrt{(x+3)^2}-\sqrt{(y-1)^2}=

= |x+3|-|y-1|=

= |\frac{3}{4}+3|-|\frac{2}{5}-1|=

= |\frac{15}{4}|-|-\frac{3}{5}|=

= \frac{15}{4}-\frac{3}{5}=

= \frac{63}{20}

Answer: B.

The point here is that square root function cannot give negative result →

\sqrt{some \ expression}\geq{0}

. For example,

\sqrt{x^2}\geq{0}

→

\sqrt{25}=5

(not +5 and -5). In contrast, the equation

x^2=25

has TWO solutions, +5 and -5, because both 5^2 and (-5)^2 equal to 25.…

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What this question tests

What it tests

Your handling of square and higher roots, including simplifying radicals.

Common trap

Forgetting the ± when taking a square root to solve an equation, or assuming √(a²) = a.

If x=34x=\frac{3}{4}x=43​ and y=25y=\frac{2}{5}y=52​, what is the value of x2+6x+9−y2−2y+1\sqrt{x^2 +6x +9}-\sqrt{y^2 -2y +1}x2+6x+9​−y2−2y+1​?