Answer:X=i and ±[tex]\sqrt{\frac{7}{9} }[/tex]
Step-by-step explanation:
Answer : The solutions of the equation are, [tex]x=\pm i\sqrt{\frac{7}{9}}[/tex] and [tex]x=\pm 1[/tex]
Step-by-step explanation :
As we are given that the expression of equation as:
[tex]9x^4-2x^2-7=0[/tex]
Let [tex]x^2=u[/tex], we get:
[tex]9u^2-2u-7=0[/tex]
Now split this expression by middle term splitting method.
[tex]9u^2-9u+7u-7=0[/tex]
[tex]9u(u-1)+7(u-1)=0[/tex]
[tex](9u+7)(u-1)=0[/tex]
(9u+7) = 0 and (u-1) = 0
[tex]u=\frac{-7}{9}[/tex] and u = 1
As,
[tex]x^2=u[/tex]
Thus, the value of 'x' for [tex]u=\frac{-7}{9}[/tex] is:
[tex]x^2=u=\frac{-7}{9}[/tex]
[tex]x^2=\frac{-7}{9}[/tex]
[tex]x=\sqrt{\frac{-7}{9}}[/tex] [tex](i^2=-1)[/tex]
[tex]x=\pm i\sqrt{\frac{7}{9}}[/tex]
The value of 'x' for [tex]u=1[/tex] is:
[tex]x^2=u=1[/tex]
[tex]x^2=1[/tex]
[tex]x=\pm 1[/tex]
Therefore, the solutions of the equation are, [tex]x=\pm i\sqrt{\frac{7}{9}}[/tex] and [tex]x=\pm 1[/tex]
