Question

preciso das contas :
1) x² + 2x =35
2)x² - 5 =104
3)x² + (x + 1)² =481
4) x(x + 5)=84
5) (5 + x)²=49

Answer 1

1) x² + 2x =35
x²+2x-35=0
Δ = b² - 4.a.c 
Δ = 2² - 4 . 1 . -35 
Δ = 4 - 4. 1 . -35 
Δ = 144

Aplicando Bhaskara:
x' = (-2 + √144)/2.1   x' = 10 / 2  x' = 5
x'' = (-2 - √144)/2.1  x'' = -14 / 2 x'' = -7


2)x² - 5 =104
x²-5-104=0
Δ = b²  - 4.a.c 
Δ = -5²  - 4 . 1 . -104 
Δ = 25 - 4. 1 . -104 
Δ = 441

Aplicando Bhaskara:

x' = (--5 + √441)/2.1 x' = 26 / 2   x' = 13
x'' = (--5 - √441)/2.1 x'' = -16 / 2  x'' = -8

3)x² + (x + 1)² =481
x²+x²+1²-481=0
2x²+1-481=0
2x²-480=0

Δ = b²  - 4.a.c 
Δ = 0²  - 4 . 2 . -480 
Δ = 0 - 4. 2 . -480 
Δ = 3840

x' = (-0 + √3840)/2.2   x' = 61,96773353931867 / 4 
x' = 15,491933384829668

x'' = (-0 - √3840)/2.2 x'' = -61,96773353931867 / 4 
x'' = -15,491933384829668

4) x(x + 5)=84
x²+5x-84=0
Δ = b² - 4.a.c 
Δ = 5² - 4 . 1 . -84 
Δ = 25 - 4. 1 . -84 
Δ = 361

x' = (-5 + √361)/2.1  x' = 14 / 2    x' = 7
x'' = (-5 - √361)/2.1  x'' = -24 / 2   x'' = -12


5) (5 + x)²=49
25+x²-49=0
x²-24=0
Δ = b²  - 4.a.c 
Δ = 0²  - 4 . 1 . -24 
Δ = 0 - 4. 1 . -24 
Δ = 96

x' = (-0 + √96)/2.1 x' = 9,797958971132712 / 2 x' = 4,898979485566356
x'' = (-0 - √96)/2.1 x'' = -9,797958971132712 / 2  x'' = -4,898979485566356