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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+2x38=0

can be written as

(x3)2+2x38=0

If we let u=x3 this becomes even clearer:

u2+2u8=0

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

Let's see some examples.

Example

Solve the equations

  1. x66x3+8=0

  2. 7218x+x=0

Exercise

Hint
Solution