Solve. (the 4 next to the x is supposed to be an exponent)( the star means squared)
x4 - 53x* + 196 =0
Will someone help me with this math question?
2008-12-31 3:00 am
回答 (7)
2008-12-31 3:11 am
✔ 最佳答案
x^4 - 53x^2 + 196 = 0After factorising you get:
(x-7)(x+7)(x-2)(x+2) = 0
Using the null factor law, x equals:
7, -7, 2 or -2
Hope that helps.
=D
2008-12-31 11:07 am
Let y = x^2
y^2 - 53y + 196 = 0
(y - 49)(y - 4) = 0
y = 49 or 4
ây = x, therefore x = ±7 or ±2.
y^2 - 53y + 196 = 0
(y - 49)(y - 4) = 0
y = 49 or 4
ây = x, therefore x = ±7 or ±2.
2008-12-31 11:07 am
x^4 - 53x^2 + 196 =0
(x^2 - 4) ( x^2 - 49) = 0
(x +2)(x -2) (x +7)(x -7) = 0
x = -2 , x =2, x =-7, x =7
(x^2 - 4) ( x^2 - 49) = 0
(x +2)(x -2) (x +7)(x -7) = 0
x = -2 , x =2, x =-7, x =7
2008-12-31 4:54 pm
a^2 - b^2 = (a + b)(a - b)
x^4 - 53x^2 + 196 = 0
x^4 - 4x^2 - 49x^2 + 196 = 0
(x^4 - 4x^2) - (49x^2 - 196) = 0
x^2(x^2 - 4) - 49(x^2 - 4) = 0
(x^2 - 4)(x^2 - 49) = 0
(x^2 - 2^2)(x^2 - 7^2) = 0
(x + 2)(x - 2)(x + 7)(x - 7) = 0
x + 2 = 0
x = -2
x - 2 = 0
x = 2
x + 7 = 0
x = -7
x - 7 = 0
x = 7
ⴠx = ±2 , ±7
x^4 - 53x^2 + 196 = 0
x^4 - 4x^2 - 49x^2 + 196 = 0
(x^4 - 4x^2) - (49x^2 - 196) = 0
x^2(x^2 - 4) - 49(x^2 - 4) = 0
(x^2 - 4)(x^2 - 49) = 0
(x^2 - 2^2)(x^2 - 7^2) = 0
(x + 2)(x - 2)(x + 7)(x - 7) = 0
x + 2 = 0
x = -2
x - 2 = 0
x = 2
x + 7 = 0
x = -7
x - 7 = 0
x = 7
ⴠx = ±2 , ±7
2008-12-31 11:13 am
x^4 - 53x^2 + 196 = 0
(x^2 - 4)(x^2 - 49) = 0
(x + 2)(x - 2)(x + 7)(x - 7) = 0
(x + 2) = 0
x = -2
(x - 2) = 0
x = 2
(x + 7) = 0
x = -7
(x - 7) = 0
x = 7
x = {-2, 2, -7, 7}
(x^2 - 4)(x^2 - 49) = 0
(x + 2)(x - 2)(x + 7)(x - 7) = 0
(x + 2) = 0
x = -2
(x - 2) = 0
x = 2
(x + 7) = 0
x = -7
(x - 7) = 0
x = 7
x = {-2, 2, -7, 7}
2008-12-31 11:10 am
x⁴ – 53x² + 196 = 0
(x² – 4)(x² – 49) = 0
(x – 2)(x + 2)(x – 7)(x + 7) = 0
x = ±2, ±7
.
(x² – 4)(x² – 49) = 0
(x – 2)(x + 2)(x – 7)(x + 7) = 0
x = ±2, ±7
.
2008-12-31 11:08 am
replace x* with y
you get y* -53y+196=0
y1=49
y2=4
and you get:
x1=-7
x2=-2
x3=2
x4=7
four solutions, because it's a grade 4 equation
you get y* -53y+196=0
y1=49
y2=4
and you get:
x1=-7
x2=-2
x3=2
x4=7
four solutions, because it's a grade 4 equation
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