The difference of square of two number is 180. The square of smaller number is 8 times the larger number. Find the two numbers.?

Question

Answer

Problem Statement: The difference of square of two number is 180. The square of smaller number is 8 times the larger number. Find the two numbers.

Solution:

Let's assume two numbers as x and y, where x is the smaller number and y is the larger number.

Equation 1: The difference of square of two number is 180
According to the problem statement, we can write the equation as:
x^2 - y^2 = 180

Equation 2: The square of smaller number is 8 times the larger number
According to the problem statement, we can write the equation as:
x^2 = 8y

Solving the Equations:
We can use the substitution method to solve the equations.

Substituting the value of x^2 from Equation 2 in Equation 1, we get:
8y - y^2 = 180

Rearranging the equation, we get:
y^2 - 8y + 180 = 0

We can solve this quadratic equation using the quadratic formula:
y = [8 ± √(8^2 - 4*1*180)]/2
y = [8 ± √(-304)]/2

The value under the square root is negative, which means there are no real solutions for y.

Therefore, there are no real solutions for the two numbers x and y that satisfy the given conditions.

Conclusion: The given problem does not have any real solutions for the two numbers x and y.

Answer

Answer

Answer

Let us suppose two required is x and y.

Such that x > y.

According to your given condition

x^2 - y^2 = 180………(1)

And according to question

y^2 = 8x. (Put this value in above equation.)

Then above equation become

x^2 - 8x = 180.

x^2 - 8x -180 = 0

We can write as

x^2 -18x + 10x -180 = 0.

x(x - 18) + 10(x - 18) = 0

(x + 10)(x - 18) = 0
When x = -10.

100 - y^2 = 180

100 - 180 = y^2

y = √(-80)

When x = 18

324 - y^2 = 180

y^2 = 144

y = 12

Answer

Similar Class 10 Doubts

The difference of square of two numbers is 88. If the larger number is 5 less than twice the smaller number then find the two numbers?

if three times the larger of the two numbers is dividedby the smaller one, we get 4 as qoutient and 3 as remainder. Also, if seven times the number is divided by the larger one we get 5 as qoutient and 1 as remainder . find the number

Three consecutive natural numbers are such that at the square of middle number exceeds the difference of squares of other two by 60 find the numbers?

If three times the larger of two numbers is divided by the smaller one, we get 4 as quotient and 3 as remainder. If seven times the smaller number is divided by the largerone, we get 5 as the quotient and 1 as the remainder. What is the smaller number?

If a number x is chosen at random from the numbers -2,-1,0,1,2, what is the probability that x square is smaller than two?

Top Courses for Class 10View all

Science Class 10

Social Studies (SST) Class 10

Mathematics (Maths) Class 10

English Class 10

Past Year Papers for Class 10

Top Courses for Class 10

Top Courses for Class 10

Related Content

About Class 10

Class 10 Study Material

Class 10 All Subjects

NCERT Textbook Solutions

Other Classes

Important Links

Company