The difference between two numbers is 2. Their product is 84 greater than the square of the smaller number. The sum of the number is_______

164

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Solution

The correct option is B 86
Let x be the largest and y be the smallest number.
Therefore, according to question
$x - y = 2 \Rightarrow x = y + 2$ ...(i)
Also, given $x y = 84 + y^{2}$
$(y + 2) y = 84 + y^{2}$ ( $∵$ of (i))
$\Rightarrow y^{2} + 2 y = 84 + y^{2}$
$\Rightarrow 2 y = 84 \Rightarrow y = 42$
and from (i),
$x = 42 + 2 = 44$
$∴ x + y = 44 + 42 = 86$
Therefore, option B is correct.

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The difference between two numbers is 2. Their product is 84 greater than the square of the smaller number. The sum of the number is_______

The correct option is B 86Let x be the largest and y be the smallest number.Therefore, according to questionx−y=2⇒x=y+2 ...(i)Also, given xy=84+y2(y+2)y=84+y2 (∵ of (i))⇒y2+2y=84+y2⇒2y=84⇒y=42and from (i),x=42+2=44∴x+y=44+42=86Therefore, option B is correct.