Question

find two positive numbers whose sum is 21 and sum of whose squares is 261

Answer 1

Answer:

Let one number be x.

Then, other no = ( 21 - x )

Now, it is given that, sum of it's square is 261.

x² + (21 - x)² = 261

⇒ x² + (21)² + x² - 2 * x * 21 = 261

⇒ 2x² + 441 - 42x = 261

⇒ 2x² - 42x + 441 - 261 = 0

⇒ 2x² - 42x + 180 = 0

⇒ 2 (x² - 21x + 90) = 0

⇒ x² - 21x + 90 = 0

⇒ x² - 15x - 6x + 90 = 0

⇒ x ( x - 15 ) - 6 ( x - 15 ) = 0

⇒ ( x - 15 ) ( x - 6 ) = 0

⇒ x = 15 or x = 6

Hence, the answer is 15 and 6.

Answer 2

Heya!

Let that two numbers be x and y

ACCORDING TO THE GIVEN QUESTION

x + y = 21 ... Equation ( i )

x² + y² = 261 ... Equation ( ii )

SQUARING ON BOTH SIDES IN EQUATION ( i ) WE HAVE

x² + y² + 2xy = 441

261 + 2xy = 441

2xy = 180

xy = 90

y = 90/x ... Equation ( iii )

FROM EQUATION ( i ) AND ( iii ) WE HAVE.

x² - 21x + 90 = 0

x² - 15x - 6x + 90 = 0

x( x - 15 ) -6 ( x - 15 ) = 0

x = 15 OR x = 6

For x = 15 y = 6

For x = 6 y = 15

So, the two numbers are 15 and 6

Or

6 And 15