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Callum Martyn
Looking to sell a business in the Devon area
3 months ago
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We have an established network of business buyers and we can help you sell your business in the shortest possible time and at a price you can afford.Q:
How to solve the following inequality: $5sqrt[4]{2}-3sqrt[3]{3}le 0$
I am trying to solve this inequality.
$$5sqrt[4]{2}-3sqrt[3]{3}le 0$$
Thank you for your help in advance.
A:
(1) We have $sqrt[3]{3}= rac{sqrt[3]3+sqrt[3]3}2geq rac13+ rac{sqrt[3]3}2= rac{sqrt[3]3}2geq rac12$. Hence, $5sqrt[4]{2}-3sqrt[3]{3}leq5sqrt[4]2-2cdot rac{sqrt[3]3}2leq5sqrt[4]2-2cdot rac12=2cdot rac12= rac14$.
(2) The solution is $2$. This is because, the real roots of the LHS are $(-infty,0)$, so $x^4-2x^3+5x^2-3x+2=x^4-x^3-x^2+2x