<h2><u>Q</u><u>u</u><u>e</u><u>s</u><u>t</u><u>i</u><u>o</u><u>n</u>:-</h2>
The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.
<h2><u>S</u><u>o</u><u>l</u><u>u</u><u>t</u><u>i</u><u>o</u><u>n</u>:-</h2>
Let the larger number be x
And, the square of the smaller number be 8x
<h3><u>A</u><u>T</u><u>Q</u> ,</h3>
x² − 8x = 180
⇒ x² − 8x − 180 = 0
⇒ x² − (18 − 10)x − 180 = 0
⇒ x² − 18x + 10x − 180 = 0
⇒ x (x − 18) + 10(x − 18) = 0
⇒ (x − 18) (x + 10) = 0
⇒ x − 18 = 0, x + 10 = 0
⇒ x = 18, x = −10
⇒ x = −10, 18
Either, x = −10 and x = 18
x = 18 (Positive value)
Now, the square of the smaller number = 8x = 8 × 18 = 144
So, the square of the smaller number = = 12
<h3>The two numbers are <u>1</u><u>8</u><u> </u><u>a</u><u>n</u><u>d</u><u> </u><u>1</u><u>2</u>. [Answer]</h3>