Question

Find two numbers whose sum is 27 and product is 182​

Answer 1

Answer:

Let the first number be x and the second number is 27 - x.

Therefore, their product = x (27 - x)

It is given that the product of these numbers is 182.

Therefore, x(27 - x) = 182

⇒ x2 – 27x + 182 = 0

⇒ x2 – 13x - 14x + 182 = 0

⇒ x(x - 13) -14(x - 13) = 0

⇒ (x - 13)(x -14) = 0

Either x = -13 = 0 or x - 14 = 0

⇒ x = 13 or x = 14

If first number = 13, then

Other number = 27 - 13 = 14

If first number = 14, then

Other number = 27 - 14 = 13

Therefore, the numbers are 13 and 14

HOPE IT HELPS YOU!!

HAVE A GREAT DAY!!

Answer 2

$\orange{\mathcal{\underline{\underline{Given:-}}}}$

• Two Numbers Whose Sum is 27 and Product is 182

$\orange{\mathcal{\underline{\underline{To \: find:-}}}}$

• The Numbers

$\rm \underline{ \blue{ \boxed{ \bf \red{Solution:}}}}$

Suppose that Numbers Are x and y

$\</strong>s<strong>f</strong><strong>{</strong><strong>x</strong><strong>+</strong><strong>y</strong><strong>=</strong><strong>2</strong><strong>7</strong><strong>}$

$\sf{x=27</strong><strong>-</strong><strong>y</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>.</strong><strong>.</strong><strong>.</strong><strong>(</strong><strong>i</strong><strong>)</strong><strong>}$

$\sf{</strong><strong>xy</strong><strong>=</strong><strong>1</strong><strong>8</strong><strong>2</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>.</strong><strong>.</strong><strong>.</strong><strong>(</strong><strong>ii</strong><strong>)</strong><strong>}$

$\</strong><strong>r</strong><strong>m</strong><strong>\</strong><strong>g</strong><strong>r</strong><strong>e</strong><strong>e</strong><strong>n</strong><strong>{</strong><strong>Substitute</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>Value</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>Of</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>x</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>in</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>(</strong><strong>ii</strong><strong>)</strong><strong>}$

We Get,

$\sf{</em></strong><strong><em>(</em></strong>27-y<strong><em>)</em></strong><strong><em>y</em></strong><strong><em>=</em></strong><strong><em>1</em></strong><strong><em>8</em></strong><strong><em>2</em></strong><strong><em>}</em></strong><strong><em>$

$\sf{</em></strong><strong><em>27y - {y}^{2} = 182</em></strong><strong><em>}</em></strong></p><p></p><p><strong><em>$

$\sf{</em></strong><strong><em>{y}^{2} - 27y - 182 = 0</em></strong><strong><em>}$

$\sf{</em></strong><strong><em>{y}^{2} - 14y - 13y - 182 = 0</em></strong><strong><em>}$

$\sf{y(y - 14) - 13(y - 14) = 0}$

$\sf{(y - 14) (y - 13) = 0}$

$\sf{y=14,13}$

$\rm\green{Substitute \: Value \: Of \: y=14 \: in \: (i)}$

$\sf{x+y=27}$

$\sf{x+14=27}$

$\sf{x=13}$

$\bf\purple{x=13,y=14 \: \: Or \: \: x=14,y=13}$

$\sf\pink\bigstar{Verification}\pink\bigstar$

$\sf{13+14=27}$

$\sf{13×14=182}$

$\sf\blue\checkmark{Verified}\blue\checkmark$