Question

please solve this question fast ​

Answer 1

answer of your question is 90

Answer 2

Answer:

90

Step-by-step explanation:

Method 1

For a quadratic ax²+bx+c, the sum of the roots is -b/a and the product of the roots is c/a.

As α and β are roots of x² - 4x + 3, we have

α + β = 4   and   αβ = 3

=> α² + β² = ( α + β )² - 2αβ = 4² - 2×3 = 16 - 6 = 10

=> α⁴β² + α²β⁴ = α²β² ( α² + β² ) = (αβ)² ( α² + β² ) = 3² × 10 = 90

Method 2

Factorize the quadratic: x² - 4x + 3 = ( x - 1 ) ( x - 3 ).

So the roots are 1 and 3.  Taking α=1 and β=3 then gives

α⁴β² + α²β⁴ = 1⁴×3² + 1²×3⁴ = 9 + 81 = 90