how it solve math questiona?
回答 (10)
2008-09-11 3:56 pm
✔ 最佳答案
√x+6=xmove 6 to the other side
√x=x-6
()²
x = ( x-6)²
x= x² - 12x + 36
x² -13x + 36 =0
(x-4) (x-9) =0
x=4
or
x=9
but we have to prove every single solution , couse if we use ()²
we may get a wrong answer too.
for x=4
√4+6=4
8=4 is wrong
for x=9
√9+6=9
9=9 is true
2008-09-11 10:58 pm
â(x + 6) = x
x + 6 = x²
x² - x = 6
x² - 1/2x = 6 + (- 1/2)²
x² - 1/2x = 24/4 + 1/4
(x - 1/2x)² = 25/4
x - 1/2 = 5/2
1st value of x:
x = 5/2 + 1/2
x = 3
2nd value of x:
x = - 5/2 + 1/2
x = - 2
Answer: x = 3, - 2
Proof (x = 3):
â(3 + 6) = 3
â9 = 3
3 = 3
Proof (x = - 2):
â(- 2 + 6) = - 2
â4 = - 2
- 2 = - 2
x + 6 = x²
x² - x = 6
x² - 1/2x = 6 + (- 1/2)²
x² - 1/2x = 24/4 + 1/4
(x - 1/2x)² = 25/4
x - 1/2 = 5/2
1st value of x:
x = 5/2 + 1/2
x = 3
2nd value of x:
x = - 5/2 + 1/2
x = - 2
Answer: x = 3, - 2
Proof (x = 3):
â(3 + 6) = 3
â9 = 3
3 = 3
Proof (x = - 2):
â(- 2 + 6) = - 2
â4 = - 2
- 2 = - 2
2008-09-11 10:54 pm
âx + 6 = x
âx = (x  – 6)
squaring both sides
x = x² – 12x + 36
x² – 13x + 36 = 0
(x – 9)(x– 4) = 0
x = 9 or x = 4
-----------
âx = (x  – 6)
squaring both sides
x = x² – 12x + 36
x² – 13x + 36 = 0
(x – 9)(x– 4) = 0
x = 9 or x = 4
-----------
2008-09-11 11:15 pm
(âx+6=x)^2
x+6=x^2
x^2-x-6=0
(x-3)(x+2)=0
x=3 or x=-2
but x=-2 is impossible because the square root of something is always a positive number.
So, x=3
x+6=x^2
x^2-x-6=0
(x-3)(x+2)=0
x=3 or x=-2
but x=-2 is impossible because the square root of something is always a positive number.
So, x=3
2008-09-11 11:06 pm
â(x + 6) = x
x + 6 = x^2
x^2 - x - 6 = 0
x^2 + 2x - 3x - 6 = 0
(x^2 + 2x) - (3x + 6) = 0
x(x + 2) - 3(x + 2) = 0
(x + 2)(x - 3) = 0
x + 2 = 0
x = -2
x - 3 = 0
x = 3
â´ x = -2 , 3
x + 6 = x^2
x^2 - x - 6 = 0
x^2 + 2x - 3x - 6 = 0
(x^2 + 2x) - (3x + 6) = 0
x(x + 2) - 3(x + 2) = 0
(x + 2)(x - 3) = 0
x + 2 = 0
x = -2
x - 3 = 0
x = 3
â´ x = -2 , 3
2008-09-11 11:00 pm
âx+6=x
âx = x-6
square both sides
x = (x-6)^2
x = x^2-12x+36
x^2-13x+36=0
x^2-4x-9x+36=0
x(x-4)-9(x-4)=0
(x-4)(x-9)=0
x=4
x=9
âx = x-6
square both sides
x = (x-6)^2
x = x^2-12x+36
x^2-13x+36=0
x^2-4x-9x+36=0
x(x-4)-9(x-4)=0
(x-4)(x-9)=0
x=4
x=9
2008-09-11 10:58 pm
x+6=x^2
x^2-x-6=0
on solving this quadratic equation we get
ans
x=3,-2
x^2-x-6=0
on solving this quadratic equation we get
ans
x=3,-2
2008-09-11 10:51 pm
x = 9
2008-09-11 10:51 pm
âx+6=x
x - âx - 6 = 0
(âx - 3)(âx + 2) = 0
âx = 3, -2
x = 9, 4
x - âx - 6 = 0
(âx - 3)(âx + 2) = 0
âx = 3, -2
x = 9, 4
2008-09-11 10:49 pm
X=9
square root of 9 is 3 plus 6 equals nine again...i don't know how to tell you the formula, but, i was a genious in math at school..i could solve the problems, but couldn't tell you the methods my mind uses to acquire the answers, but, here the answere is 9=X
square root of 9 is 3 plus 6 equals nine again...i don't know how to tell you the formula, but, i was a genious in math at school..i could solve the problems, but couldn't tell you the methods my mind uses to acquire the answers, but, here the answere is 9=X
收錄日期: 2021-05-01 11:16:17
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20080911074409AAmFNXa