The sum of square of two number is 130 the sum of smaller number and twice of larger number is 25
Answers
The smaller and larger number is 2.2 or 7.8 and 11.4 or 8.6.
Given - Sum
Find - Smaller and larger number
Solution - Let the smaller number be x and larger number be y.
Forming equations according to given information-
x² + y² = 130 : Equation 1
x + 2y = 25 : Equation 2
x = 25 - 2y
Keep the value of x from equation 2 in equation 1
(25 - 2y)² + y² = 130
Solving the first bracket
625 + 4y² -100y + y² = 130
5y² - 100y + 625 - 130 = 0
5y² - 100y + 490 = 0
Dividing the equation by 5
y² - 20y + 98 = 0
Solving the quadratic equation
y = (-(-20)±✓(-20)²-4×1×98))/2×1
On solving we get the value of y -
y = 11.4 and 8.6
So, the larger number can be 11.4 of 8.6.
Small number if large number is 11.4
Small number = 25 - 2×11.4
Small number = 25 - 22.8
Small number = 2.2
Small number if large number is 8.6
Small number = 25 - 2×8.6
Small number = 25 - 17.2
Small number = 7.8
Thus, the large number can be 11.4 or 8.6 and small number can be 2.2 or 7.8
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