What are the two numbers whose sum is 21 and the sum of the squares is 261
Answers
Given : What are the two numbers whose sum is 21 and the sum of the squares is 261.
According to the question :
- Let "x" be one number and another number be "21 - x".
Calculations :
→ x² + (21 - x)² = 261
→ 2x² + 441 - 42x = 261
→ 2x² - 42x + 441 - 261 = 0
→ 2 (x² - 21x + 90) = 0
→ x² - 15x - 6x + 90 = 0
→ x (x - 15) - 6 (x - 15) = 0
→ (x - 15) (x - 6) = 0
→ x = 15, x = 6
Therefore, the numbers are 15 and 6.
Concept:
The polynomial equations of degree two in one variable of type f(x) = ax² + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x). The roots of the quadratic equation are the values of x that fulfil the equation (, ).
It is a given that the quadratic equation has two roots. Roots can have either a real or imaginary nature.
Given :
Sum is 21 and the sum of the squares is 261.
Find:
What are the two numbers whose sum is 21 and the sum of the squares is 261.
Solution:
According to the question :
Let "x" be one number and another number be "21 - x".
Calculations :
→ x² + (21 - x)² = 261
→ 2x² + 441 - 42x = 261
→ 2x² - 42x + 441 - 261 = 0
→ 2 (x² - 21x + 90) = 0
→ x² - 15x - 6x + 90 = 0
→ x (x - 15) - 6 (x - 15) = 0
→ (x - 15) (x - 6) = 0
→ x = 15, x = 6
Therefore, the numbers are 15 and 6
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