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Zhouningning494go
Answered

find the solution
x^4-10x^2+9=0
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Sagot :

Himarikarougo

Solve for x over the real numbers:

x^4 - 10 x^2 + 9 = 0

Substitute y = x^2:

y^2 - 10 y + 9 = 0

The left hand side factors into a product with two terms:

(y - 9) (y - 1) = 0

Split into two equations:

y - 9 = 0 or y - 1 = 0

Add 9 to both sides:

y = 9 or y - 1 = 0

Substitute back for y = x^2:

x^2 = 9 or y - 1 = 0

Take the square root of both sides:

x = 3 or x = -3 or y - 1 = 0

Add 1 to both sides:

x = 3 or x = -3 or y = 1

Substitute back for y = x^2:

x = 3 or x = -3 or x^2 = 1

Take the square root of both sides

Answer:

x = 3 or x = -3 or x = 1 or x = -1

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