Question

3. The difference of squares of two numbers is
112. The square of the smaller is 9 times the
larger number. Find the numbers.​

Answer 1

hope this answer will be helpful ♥️♥️

Answer 2

Answer:

★ 12 and 16 ★

Step-by-step explanation:

Given:

• Difference of squares of two numbers is 112.
• Square of smaller number is 9 times the larger number.

To Find:

• What are the two numbers?

Solution: Let the Larger number be x. Then the smaller number will be 9 times of x = 9x

∴ Square of larger number = x²

A/q

$\small\implies{\sf }$ x² –9x = 112

$\small\implies{\sf }$ x² –9x –112 = 0

$\small\implies{\sf }$ x² –16x + 7x –112 = 0 ( By middle term splitting)

$\small\implies{\sf }$ x ( x –16 ) + 7 ( x –16) = 0

$\small\implies{\sf }$ ( x –16) ( x + 7 ) = 0

$\small\implies{\sf }$ x –16 = 0 or x + 7 = 0

$\small\implies{\sf }$ x = 16 and x = –7

•Taking x = 16

Hence, Larger number= x = 16

∴ Smaller number = √9 times of x = √9x = √9(16) = √144 = 12

•Taking x = –7

∴ Smaller number = √9 times of x = √9x = √9(–7) = √–63 ( This is not possible)

Hence, the two numbers are 12 & 16

_____________________________

★ Check ★

→ (16)² – (12)² = 112

→ 256 – 144 = 112

→ 112 = 112 ( LHS = RHS )