Transform the following equation into quadratic equation in the form
[tex]a {x }^{2} +bx + c = 0 [/tex]
Then find the roots.
1
[tex]x(x + 5) = 2[/tex]
2
[tex]( {s + 6})^{2} = 1[/tex]
3
[tex]( {t + 2 })^{2} + ({t - 3})^{2} = 9[/tex]
4
[tex]x + \frac{8}{x - 2} = 1 + \frac{4x}{x - 2} [/tex]
5
[tex] \frac{3}{x} + \frac{4}{2x } = x - 1[/tex]
[tex]a {x }^{2} +bx + c = 0 [/tex]
Then find the roots.
1
[tex]x(x + 5) = 2[/tex]
2
[tex]( {s + 6})^{2} = 1[/tex]
3
[tex]( {t + 2 })^{2} + ({t - 3})^{2} = 9[/tex]
4
[tex]x + \frac{8}{x - 2} = 1 + \frac{4x}{x - 2} [/tex]
5
[tex] \frac{3}{x} + \frac{4}{2x } = x - 1[/tex]
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Answer:
1. x(x+5)=2
x²+5x-2=0
x=-5±√5²-4(1)(-2)
2(1)
x=-5±√25+8
2
x=-5±√33
2
x=-5+√33, -5-✓33
2 2
2. (s+6)²=1
s²+12s+36=1
s²+12s+35=0
(s+7)(s+5)=0
s=-7, -5
3. (t+2)²+(t-3)²=9
(t²+4t+4)+(t²-6t+9)=9
t²+4t+4+t²-6t+9-9=0
2t²-2t+4=0
(2t-4)(t+1)=0
t=-2,-1
4.
5.
x=1±√(-1)²-4(1)(-5)
2(1)
x=1±√1+20
2
x=1±√21
2
x= 0
x=1+√21
2
x=1-√21
2