Tentukan himpunan penyelesaian dari…

1. 2x^2 – 5x – 7 > 0

(2x – 7)( x + 1) > 0

2x -7 > 0

2x > 7

x > 7/2

x > 3,5

dicoba x = 4

(2x – 7)(x + 1)

(8 – 7)(4 + 1)

5 > 0 (benar)

x + 1 > 0

x > -1.

dicoba x = 0

(2x – 7)(x + 1)

(0 – 7)( 0 + 1)

-7 (1)

-7 < 0 (salah harusnya >0)

maka tandanya diubah jadi

x < -1

maka himpunan penyelesaian

hp = {x | x < -1 atau x > 3,5}

2. x²+10x+25=0

( x + 5 )( x + 5 )

Pembuktian

( x + 5 )( x + 5 )

x² + 5x + 5x + 25

x² + 10x + 25

Himpunan penyelesaian

x + 5 = 0

    x  = 0 -5

    x₁ = -5

x + 5 = 0

    x  = 0 – 5

    x₂ = -5

Hp = { -5 , -5 }

Semoga Membantu.

1.
( 2x – 7 ) ( x + 1 ) = 2x² + 2x – 7x – 7 = 2x² – 5x – 7

2x – 7 = 0
2x = 7
x = 7/2 = 3,5

x + 1 = 0
x = -1

HP : { 3,5 , -1 }

2.
( 5 – x ) ( x – 5 ) = 5x – 25 – x² + 5x
= -x² + 10x – 25

5 – x = 0
x = 5

x – 5 = 0
x = 5

HP : { 5 }

semoga bisa membantu ,,,,