Question

If x7 – x3 = 1542, how many values are possible for x.​

Answer 1

Answer:

there will be 7 possible values bcoz the degree of the equation decides it. A quad. equa has 2 solu, cubic equa has 3 solu similarly dis equation has 7 values

hope it helps u.....^_^

Answer 2

Given : $x^7 -x^3 = 1542$

Solution : f(x) = $x^7 -x^3$

then

f'(x) =

$7x^6-3x^2\\\\x^2(7x^4-3)$

This shows that f has an inflection point at 0

then

it is increasing over  $(-\infty, - \sqrt[4]{\frac{3}{7}})$

decreasing over $[-\sqrt[4]{\frac{3}{7}},\sqrt[4]{\frac{3}{7}}]$

increasing over $[\sqrt[4]{\frac{3}{7}}, \infty)$

Thus ,

The local maximum is

$f(-\sqrt[4]{\frac{3}{7}})= \frac{4}{7}(\sqrt[4]{\frac{3}{7}})^3<1$

i.e

it has no solution

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