Math, asked by roshni3920, 2 months ago

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

Answered by Anonymous
614

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

Answered by llMrsVampirell
3

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

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