Question

Akar akar persamaan 7x= 4x^2+3 adalah a dan b.
Nilai dari a/b + b/a = ...
a. 25/12
b. 24/12
c. 20/25
d. 16/25
e. 12/25

Sama caranya ya... makasih :)

Answer 1

Verified answer

Diket :
Persamaan kuadrat

7x = 4x² + 3
0 = 4x² - 7x + 3
Koefisien x² = 4
Koefisien x = -7
Konstanta = 3

Akar2nya a dan b

a + b = -(koefisien x)/(koefisien x²)
a + b = -(-7)/(4) = 7/4

ab = (konstanta)/(koefisien x²)
ab = 3/4

Ditanya :
a/b + b/a
= a²/ab + b²/ab
= (a² + b²)/ab
= ((a + b)² - 2ab)/ab
= ((7/4)² - 2(3/4))/(3/4)
= (49/16 - 3/2)/(3/4)
= (49/16 - 24/16)/(12/16)
= 25/12

[A]

Answer 2

Jawabannya:
a+b=-(koef x)/(koef x²)
a+b=-(-7)/(4)
a+b= 7/4

ab=(kons)/(koef x²)
ab= 3/4
jawab:
a/b+b/a
=a²/ab+b²/ab
= (a²+b²)/ab
= ((a+b)²-2ab)/ab
= ((7/4)²-2(3/4))/(3/4)
= (49/26-3/2)/(3/4)
= (49/16-24/16)/(12/16)
= 25/12 ----- A

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