Question

find two numbers whose sum is 30 and the product is 221

Answer 1

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Answer 2

Concept

In order to solve a quadratic equation, we split the middle term.

Given

two numbers whose sum is 30 and the product is 221

Find

We have to find the two numbers

Solution

Let us assume the two numbers to be x and y

Their sum will be-

x + y = 30

⇒ x = 30 - y

Their product will be-

xy = 221

substituting x = 30 - y in the above equation we get-

y (30-y) = 221

⇒ 30y - $y^{2}$ = 221

$y^{2}$ - 30y +221 = 0

$y^{2}$ - 13y - 17y + 221 = 0

y(y-13) - 17(y-13) =0

(y-13) (y-17) = 0

y = 13, 17

if y=13, x=17

and if y=17, x=13

Thus, the two numbers will be 13 and 17

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