Question

4a^2-7a+4 = 0 , then find the value if a^2 + 1/a^2 ....please solve guys

Answer 1

Answer:

$a^2+\frac{1}{a^2}=\frac{17}{16}$

Step-by-step explanation:

4a²-7a+4=0

4a²-7a=-4

dividing the equation with 4a

$a-\frac{7}{4} =\frac{-1}{a}\\\\a+\frac{1}{a}=\frac{7}{4}$

Squaring above equation on both sides

$a^2+\frac{1}{a^2}+2.a.\frac{1}{a}=\frac{49}{16}\\\\a^2+\frac{1}{a^2}=\frac{49}{16}-2\\\\a^2+\frac{1}{a^2}=\frac{49-32}{16}\\\\a^2+\frac{1}{a^2}=\frac{17}{16}$