The difference of squares of two numbers is 45
Asked by admin @ in Math viewed by 324 People
The difference of the squares of two numbers is 45 the square of the smallest number is 4 times the larger number determine the numbers.
Asked by admin @ in Math viewed by 324 People
The difference of the squares of two numbers is 45 the square of the smallest number is 4 times the larger number determine the numbers.
Answered by admin @
Answer:
Step-by-step explanation:
Solution :-
Let the larger number be x.
Then,
Square of the smaller number = 4x
Square of the larger number = x²
Difference of the squares of number = 45
According to the Question,
⇒ x² - 4x = 45
⇒ x² - 4x - 45 = 0
By using factorization method, we get
⇒ x² - 9x + 5x - 45 = 0
⇒ x(x - 9) + 5(x - 9) = 0
⇒ (x - 9) (x + 5) = 0
⇒ x - 9 = 0 or x + 5 = 0
⇒ x = 9, - 5.
When x = 9,
Square of smaller number = 4x = 4 × 9 = 36
Smaller number = ± 6
Thus, the numbers are 9 and 6 or 9 and - 6.
When x = - 5
Square of smaller number = 4x = 4 × (- 5) = - 20
Hence, the numbers are 9 and 6 or 9 and - 6.
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