The sum of squares of two numbers is 80. The square of the smaller number is 2 times the larger
number, find the two numbers.
Answers
Answer:
Two numbers are:
Smaller number = ± 4
Larger number = 8
Step-by-step explanation:
Given that:
The sum of squares of two numbers is 80.
The square of the smaller number is 2 times the larger number.
To Find:
The two numbers.
Let us assume:
Smaller number be x.
Larger number be y.
According to the question.
Square of the smaller number = 2 times the larger number
⟶ x² = 2y
⟶ y = x²/2 _____(i)
Sum of squares of two numbers = 80
⟶ x² + y² = 80
Substituting the value of y.
⟶ x² + (x²/2)² = 80
⟶ x² + x⁴/4 = 80
Taking 4 common in LHS.
⟶ (4x² + x⁴)/4 = 80
Cross multiplication.
⟶ 4x² + x⁴ = 80 × 4
⟶ 4x² + x⁴ = 320
⟶ x⁴ + 4x² - 320 = 0
⟶ (x²)² + 4x² - 320 = 0
⟶ (x²)² + 20x² - 16x² - 320 = 0
⟶ x²(x² + 20) - 16(x² + 20) = 0
⟶ (x² - 16) (x² + 20) = 0
⟶ x² = 16 or x² = - 20 (complex number)
⟶ x = √16
⟶ x = ± 4
In equation (i).
When x = 4
⟶ y = x²/2
⟶ y = (4)²/2
⟶ y = 16/2
⟶ y = 8
When x = - 4
⟶ y = x²/2
⟶ y = (- 4)²/2
⟶ y = 16/2
⟶ y = 8
We get that:
Smaller number = ± 4
Larger number = 8
Answer:
Answer:
Two numbers are:
Smaller number = ± 4
Larger number = 8
Step-by-step explanation:
Given that:
The sum of squares of two numbers is 80.
The square of the smaller number is 2 times the larger number.
To Find:
The two numbers.
Let us assume:
Smaller number be x.
Larger number be y.
According to the question.
Square of the smaller number = 2 times the larger number
⟶ x² = 2y
⟶ y = x²/2 _____(i)
Sum of squares of two numbers = 80
⟶ x² + y² = 80
Substituting the value of y.
⟶ x² + (x²/2)² = 80
⟶ x² + x⁴/4 = 80
Taking 4 common in LHS.
⟶ (4x² + x⁴)/4 = 80
Cross multiplication.
⟶ 4x² + x⁴ = 80 × 4
⟶ 4x² + x⁴ = 320
⟶ x⁴ + 4x² - 320 = 0
⟶ (x²)² + 4x² - 320 = 0
⟶ (x²)² + 20x² - 16x² - 320 = 0
⟶ x²(x² + 20) - 16(x² + 20) = 0
⟶ (x² - 16) (x² + 20) = 0
⟶ x² = 16 or x² = - 20 (complex number)
⟶ x = √16
⟶ x = ± 4
In equation (i).
When x = 4
⟶ y = x²/2
⟶ y = (4)²/2
⟶ y = 16/2
⟶ y = 8
When x = - 4
⟶ y = x²/2
⟶ y = (- 4)²/2
⟶ y = 16/2
⟶ y = 8
We get that:
Smaller number = ± 4
Larger number = 8