Find the solution \(\displaystyle\sqrt{{{7}-{2}{x}}}-\sqrt{{{x}+{2}}}=\sqrt{{{x}+{5}}}\) \(\displaystyle{3}{\left({4}^{{{x}+{3}}}\right)}^{{2}}-{23}{\left({4}^{{{x}+{3}}}\right)}-{8}={0}\)

zdebe5l8

zdebe5l8

Answered question

2022-04-06

Find the solution
72xx+2=x+5
3(4x+3)223(4x+3)8=0

Answer & Explanation

cab65699m

cab65699m

Beginner2022-04-07Added 14 answers

1)72xx+2=x+5
72x=x+2=x+5
Square both sides
(72x)2=(x+5+x+2)2
72x=(x+5)+(x+2)+2(x+5)(x+2)
72x=2x+7+2x2+7x+10
4x=2x2+7x+10
2x=x2+7x+10
Square both sides
9x2=x2+7x+10
3x27x+10=0
3x2+3x10x+10=0
3x(x+1)10(x+1)=0
(x+1)(3x10)=0
x=1, x=103
But 103 doesn't satisfy the equation
Hence, the solution is x[1]
Dubliddissefyf8

Dubliddissefyf8

Beginner2022-04-08Added 10 answers

Given:
2)3(4x+3)223(4x+3)8=0
Let 4x+3=z
3z223z8=6
3z224z+z8=0
3z(z8)+1(z8)=0
(z8)(3z+1)=0
z=8, z=13
Thus, z=84x+3=8
22(x+3)=23
2x+3=3x+3=32
x=323=32
Hence, the solution is x=32

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