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polet [3.4K]
3 years ago
11

One number is 6 more than anouther number. the sum of their squares is 90

Mathematics
1 answer:
Flura [38]3 years ago
6 0
Let x = greater number
      y = smaller  number

(1) x = y + 6

(1) y = x-6

(2) x^{2} + y^{2} = 90
We'll substitute y in (1) to (2)
(2) x^{2} +  (x-6)^{2} = 90
     x^{2} +  (x^{2} - 12x + 36) = 90
     x^2 + x^2 -12x + 36 - 90 = 0
     2x^2 - 12x -54 = 0

     2(x^2 - 6x - 27) = 0
     2(x - 9)(x + 3) = 0
 x - 9 = 0        or      x + 3 = 0
      x = 9                        x = -3
and
 y = x - 6                  y = x - 6
 y = 9 - 6                  y = -3 - 6
 y = 3                        y = -9

Therefore, the two numbers can be 9 and 3 or -3 and -9.

      
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