10^(x-1)≤10^(2-2x)
x-1≤2-2x
x+2x≤2+1
3x≤3
x≤1
x∈(-∞;1]
1) -х^2+6x-58=0 I *(-1)
x^2-6x+58=0
a=1, b=-6, c=58
b^2-4ac=(-6)^2-4*1*58=36-232=-196 - нет действительных корней
2) 3х^2-2x-1=0
a=3, b=-2, c=-1
b^2-4ac=(-2)^2-4*3*(-1)=4+12=16^2
x1=2-4/6=-2/6
x2=2+4/6=6/6=1
3)-x^2+6x-5=0 I *(-1)
x^2-6x+5=0
a=1, b=-6, c=5
b^2-4ac=(-6)^2-4*1*5=36-20=16^2
x1=6-4/2=2/2=1
x2=6+4/2=10/2=5
№2
в)x^2 +64=0
x^2 = - 64
/x/=√64
x= 8 x= - 8
Ответ: 8 ; - 8.
г) 3x^2 - 15=0
3x^2 = 15
x^2 = 5
/x/ = √5
x=√5 x= - √5
Ответ: √5 ; -√5
№3
x^2-3x-10=0
D=b^2 - 4ac = ( -3)^2 - 4 * 1 * ( - 10) = 9+40=49
√D=7
x1=3+7 / 2 = 5
x2= 3 - 7 / 2 = ⇒ - 2 - Является .
Ответ: 5; - 2
№4
![( \sqrt{5}- \sqrt{2})^2=( \sqrt{6})^2-2 \sqrt{5}* \sqrt{2}+( \sqrt{2})^2=5- 2\sqrt{10}+2=7+2 \sqrt{10}](https://tex.z-dn.net/?f=%28+%5Csqrt%7B5%7D-+%5Csqrt%7B2%7D%29%5E2%3D%28+%5Csqrt%7B6%7D%29%5E2-2+%5Csqrt%7B5%7D%2A+%5Csqrt%7B2%7D%2B%28+%5Csqrt%7B2%7D%29%5E2%3D5-+2%5Csqrt%7B10%7D%2B2%3D7%2B2+%5Csqrt%7B10%7D+)
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![(4- \sqrt{10})(4+ \sqrt{10})=(4^2-( \sqrt{10})^2)=16-10=6](https://tex.z-dn.net/?f=%284-+%5Csqrt%7B10%7D%29%284%2B+%5Csqrt%7B10%7D%29%3D%284%5E2-%28+%5Csqrt%7B10%7D%29%5E2%29%3D16-10%3D6)
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