3. The difference of squares of two numbers is
112. The square of the smaller is 9 times the
larger number. Find the numbers.
Answers
Step-by-step explanation:
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 )
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