Question

1) √9-144х²2)√64+х(х+16)3)√36-4х-х²4) √3х²+2х-55)х²-16<06) х²-95≤07)х²+1>0

Answer 1

1)√9-144х²

(√9-144х²)²

9-144х²=0

-144x²=-9 |:(-9)

16x²=1

x²=+-4

 

2)√64+х(х+16)

(√64+х(х+16))²

64+х(х+16)

64+x^2+16x=0

x^2+16x+64=0

D=16^2-4*1*64=256-256=0

 

3)√36-4х-х²

(√36-4х-х²)^2

36-4х-х²

-x^2-4x+36=0 |:(-1)

x^2+4-36=0

D=4^2-4*1*(-36)= 16+144=160

x12=-4+-160/2

x1=-4+160/2=78

x2=-4-160/2=-82

 

4)√3х²+2х-5

(√3х²+2х-5)^2

3х²+2х-5=0

D= 2^2-4*1*(-5)=4+20=24

x12=-2+-24/2

x1=-2+24/2=11

x2=-2-24/2=13

 

5)х²-16<0

х²<+-4

 

   

 

Answer 2

1) √9 - 144х² = 3 - 144х² 2) √64 + х(х+16) = 8 + х(х+16) 3) √36 - 4х - х² = 6 - 4х - х² 4) √3х² + 2х - 5 = √3х² + 2х - 5 5) х² - 16 < 0 -> (х-4)(х+4) < 0 -> -4 < x < 4 6) х² - 95 ≤ 0 -> х² ≤ 95 -> -√95 ≤ x ≤ √95 7) х² + 1 > 0 -> х² > -1 -> for all real x