perplexus.info :: Just Math : Quad composition

Quad composition (Posted on 2019-03-16)

Let f(x)=x²+10x+20, find the number of real solutions satisfying f(f(f(f(x))))=0

No Solution Yet Submitted by Danish Ahmed Khan

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Little addition

Comment 4 of 4 |

Just to say that the roots are:

y=f(x)

x1=-5+sqrt(5)

x2=-5-sqrt(5)

y=f(f(x))

x1=-5+sqrt(sqrt(5))

x2=-5-sqrt(sqrt(5))

y=f(f(f(x)))

x1=-5+sqrt(sqrt(sqrt(5)))

x2=-5-sqrt(sqrt(sqrt(5)))

y=f(f(f(f(x))))

x1=-5+sqrt(sqrt(sqrt(sqrt5))))=6.105823

x2=-5-sqrt(sqrt(sqrt(sqrt(5))))=3.894176

Posted by armando on 2019-03-17 17:42:12

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