Question

Jika x1 & x2 ad akar* persamaan kuadrat x pngkt 2-7x+5=0 tentukan .
a.4x1 + 4x2
b.x1 pngkt kuadrat × x2 + x1×x2 pngkt kuadrat
c.1/x1 +1/x2
d.x1/x2 +x2/x1
e.x1 pngkt kuadrat + x2 pngkt kuadrat
f.(x1-x2) pngkt kuadrat
g. x1 pngkt 3 + x2 pngkt 3 ? tolong thanks

Answer 1

X² - 7x + 5 = 0
a= 1 , b= -7 , c = 5
x1 + x2 = -b/a = 7
x1 x2 = c/a = 5
a. 4x1 + 4 x2 = 4 (x1 + x2) = 4 (7) = 28
b. x1²x2 + x1 x2² = x1x2 (x1 + x2) = 5 (7) = 35
c. 1/x1 + 1/x2 = (x2 + x1)/(x1x2) = 7 / 5
d. x1/x2 + x2/x1 = (x1²+x2²)/x1x2 = ( (x1+x2)² - 2x1x2)/ x1x2
   = ( (7² - 2(5)) / 5 = 39 / 5
e. x1² + x2² = (x1 + x2)² - 2x1 x2 = 7² - 2(5) = 49 - 10 = 39
f. (x1 - x2)² = (x1 + x2)² - 4x1 x2 = 7² - 4(5) = 49 - 20 = 29
g. (x1³ + x³) = (x1 + x2)³ - 3x1²x2 - 3x1x2² = (x1+x2)³ - 3(x1x2)(x1 + x2)
      = 7³ - 3(5)(7) = 343 - 105 = 238