Question

Persamaan kuadrat yang akar akarnya 5 + akar6 dan 5 - akar6 adalah...

a. X^2 - 10x + 19 = 0
b. x^2 + 19x - 10 = 0
c. x^2 + 10x - 19 = 0
d. x^2 - 19x + 10 = 0
e. x^2 - 10x - 19 = 0

Answer 1

X = 5 + √6
x - 5 - √6 = 0

x = 5 - √6
x - 5 + √6 = 0

(x - 5 - √6) (x - 5 + √6)
= (x)(x) + (x)(-5) + (x)(√6) + (-5)(x) + (-5)(-5) + (-5)(√6) + (-√6)(x) + (-√6)(-5) + (-√6)(√6)
= x² - 5x + √6x - 5x + 25 - 5√6 - √6x + 5√6 - 6
= x² - 5x - 5x + √6x - √6x - 5√6 + 5√6 + 25 - 6
= x² - 10x + 25 - 6
= x² - 10x + 19

x² - 10x + 19 = 0

Answer 2