Question

please if anyone knows how to solve it just drop ur answer ​

Answer 1

Answer:

Step-by-step explanation:

//We know that in a quadratic equation of form ax²+bx+c, where α and β are the roots,

Sum of roots = α + β = -b/a

Product of roots = αβ = c/a

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so in equation x² + x - 1,  a = 1, b = 1, c = -1

Sum of roots = α + β = - b/a = -1/1 = -1

Product of roots = αβ = c/a = -1/1 = -1.

1) 1/α + 1/β

//taking LCM

=> α + β/αβ

=> -1/-1

=> 1

2) α/β + β/α

//Taking LCM

=> α² + β²/αβ

//We know the identity (a+b)² = a² + b²+ 2ab => a² + b² = (a + b)² - 2ab

=> (α + β)² - 2αβ / αβ

=> (-1)² - 2(-1) / -1

=> 1 + 2 / -1

=> 3/-1

=> -3.