Question

Solve the problem x⁴-13x²+42=0

Answer 1

Answer:

x = ± √6 , ± √7

Note:

★ The possible values of the variable which satisfy the equation are called its roots .

★ A biquadratic equation can have atmost four roots .

Solution:

Here,

The given equation is ;

x⁴ - 13x² + 42 = 0

We need to find the possible values x which satisfy the equation .

Thus,

Here we go ↓

=> x⁴ - 13x² + 42 = 0

=> x⁴ - 7x² - 6x² + 42 = 0

=> x²(x² - 7) - 6(x² - 7) = 0

=> (x² - 7)(x² - 6) = 0

=> x² - 7 = 0 , x² - 6 = 0

=> x² = 7 , x² = 6

=> x = ± √7 , x = ± √6

Hence,

x = ± √6 , ± √7