The square of 9 more than a number is equal to 9 more...?

2008-07-07 4:07 pm
...than the square of the number. What is the number

回答 (10)

2008-07-07 4:18 pm
✔ 最佳答案
Let x be the number.
square of 9 more than x =(x+9)^2
9 more than the square of x = x^2+9
(x+9)^2=x^2+9
x^2+18x+81=x^2+9
18x = -74
x=-4

check : (-4+9)^2=5^2=25 and (-4)^2+9= 16+9=25
2008-07-07 4:26 pm
n = the number

9^2 + n = 9 + n^2
81 + n = 9 + n^2
n^2 - n - 81 + 9 = 0
n^2 - n - 72 = 0
n^2 + 8n - 9n - 72 = 0
(n^2 + 8n) - (9n + 72) = 0
n(n + 8) - 9(n + 8) = 0
(n + 8)(n - 9) = 0

n + 8 = 0
n = -8

n - 9 = 0
n = 9

∴ n = -8 , 9
2008-07-07 4:22 pm
-4
2008-07-07 4:20 pm
-4
2008-07-07 4:14 pm
Let the number be x

(x + 9)^2 = 9 + x^2
x^2 + 18x + 81 = 9 + x^2
18x = -72
x = -4

There's your answer.
2008-07-07 4:13 pm
(x+9)² = x²+9

x²+18x+81 = x²+9

18x = -72

x=-4

Check: (-4+9)² = (-4)²+9?
5² = 16+9?
25=25

The number is -4.
2008-07-07 4:13 pm
-4
2008-07-07 4:13 pm
(x+9)^2 = x^2 + 9
x^2 + 18x + 81 = x^2 + 9
18x = -72
x = -4
2008-07-07 4:11 pm
-4 and 5 work for me.
2008-07-07 4:11 pm
hmm 2 years of college calculus and i still cant figure this out. what a useless problem


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