Question

Solve x4 – 17x2 + 16 = 0.

Answer 1

So, values of x are:

x = 1

x = -1

x = 4

x = -4

Step-by-step explanation:

Solving the equation:

$x^4-17x^2 + 16 = 0$

For solving the above equation, let u=x^2 and u^2=x^4

Placing values and solving:

$u^2-17u+16=0\\u^2-16u-u+16=0\\u(u-16)-1(u-16)=0\\(u-1)(u-16)=0\\u-1=0\,\,and\,\,u-16=0\\u=1\,\,and\,\,u=16$

Putting back the value of u i.e, u=x^2

$x^2=1\,\,and\,\,x^2=16\\Taking\,\,square\,\,root:\\\sqrt{x^2}=\sqrt{1}\,\,and\,\,\sqrt{x^2}=\sqrt{16}\\x=\pm 1\,\,and\,\,x=\pm 4$

So, values of x are:

x = 1

x = -1

x = 4

x = -4

Keywords: Solving the equations

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