Find all real solutions for: 3 x </mrow> 2 x

excluderho

excluderho

Answered question

2022-06-18

Find all real solutions for:
3 x 2 x 2 7 x + 7 + 27 x 2 x 2 + 6 x + 7 = 8

Answer & Explanation

Sawyer Day

Sawyer Day

Beginner2022-06-19Added 30 answers

Let  A = 2 x 2 + 6 x + 7
3 x A 13 x + 27 x A = 8
3 A x + 27 x ( A 13 x ) = 8 A ( A 13 x )
3 A x + 27 A x 351 x = 8 A 2 104 A x
8 A 2 134 A x + 351 x = 0
( 4 A 13 x ) ( 2 A 27 x ) = 0
4 A 13 x = 0
8 x 2 + 24 x + 28 13 x = 0
8 x 2 + 11 x + 28 = 0
Δ < 0 No real solutions
2 A 27 x = 0
4 x 2 + 12 x + 14 27 x = 0
4 x 2 15 x + 14 = 0 x = 2 , 7 4

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