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Log(2)x*log(2)(32x)=log(2)x*(log(2)x+5)=log²(20x+5log(20x
Ответ: x=7.
Объяснение:
1+√(1+x*√(x²-24))=x
√(1+x*√(x²-24))=x-1
ОДЗ:
{x-1≥0 {x≥1 x∈[1;+∞)
{x²-24≥0 {x²≥24 x²-24≥0 (x-√24)(x+√24)≥0
x∈(-∞;-2√26]U[2√6;+∞) ⇒ x∈[2√6;+∞).
(√(1+x*√(x²-24)))²=(x-1)²
1+x*√(x²+24)=x²-2x+1
x*√(x²-24)=x²-2x
x*√(x²-24)-x²+2x=0
x*(√(x²-24)-x+2)=0
x=0 ∉ОДЗ
√(x²-24)-x+2=0
√(x²-24)=x-2
(√(x²-24))²=(x-2)²
x²-24=x²-4x+4
4x=28 |÷4
x=7 ∈ ОДЗ.
У=-3+1,5х и у=17/3-2/3х
-3+1,5х =17/3-2/3х
3/2х+2/3х=17/3+3
9/6х+4/6х=26/3
13/6х=26/3
х=26/3:13/6=26/3*6/13=4
у=-3+1,5*4=-3+6=3