Question 71

If x + y = 15 and xy = 14, then the value of x — y is:

Solution

Given, $$x+y\ =15$$ and $$xy=14$$

$$=$$> $$\left(x+y\right)^2=15^2$$

$$=$$> $$x^2+y^2+2xy=225$$

$$=$$> $$x^2+y^2+2xy-2xy+2xy=225$$

$$=$$> $$x^2+y^2-2xy+4xy=225$$

$$=$$> $$\left(x-y\right)^2+4\left(14\right)=225$$

$$=$$> $$\left(x-y\right)^2+=225-56$$

$$=$$> $$\left(x-y\right)^2+=169$$

$$=$$> $$x-y=13$$

Hence, the correct answer is Option A

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