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Show that the equation x cubed + 8x = 30 has a solution between x = 2.2 and x =2.3 ?

Sagot :

konrad509
[tex]x^3+8x=30\\ x^3+8x-30=0\\\\ 2.2^3+8\cdot2.2-30=10.648+17.6-30=-1.752\\ 2.3^3+8\cdot2.3-30=12.167+18.4-30=0.567 [/tex]

For [tex]x=2.2[/tex] the value of [tex]x^3+8x-30[/tex] is negative, and for [tex]x=2.3[/tex] the value is positive which means between [tex]x=2.2[/tex] and [tex]x=2.3[/tex] there is an x for which the value of [tex]x^3+8x-30[/tex] is equal to 0 and therefore there is a solution.
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