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Quadratics in disguise ​

Notes ​

Sometimes, an equation can have a quadratic structure even if it is not a quadratic. For example,

x6+2x3−8=0

can be written as

(x3)2+2x3−8=0

If we let u=x3 this becomes even clearer:

u2+2u−8=0

If we can find u, then we can find x3 and hence x.

Let's see some examples.

Example ​

Solve the equations

  1. x6−6x3+8=0

  2. 72−18x+x=0

Exercise ​