Question

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a-(4x+1) ²=(3x-7)²
b- x²+(x+1)²=25
c-x²+(x-3)²=(x+3)²
d- 3x²+3=(2x+1)²+4

Answer 1

Boa tarde

a)

(4x + 1)² = (3x - 7)²

16x² + 8x + 1 = 9x² - 42x + 49 

7x² + 50x - 48 = 0 

d² = 2500 + 4*7*48 = 3844 
d = 62

x1 = (-50 +  62)/14 = 6/7
x2 = (-50 - 62)/14 = -8 

b)

x² + (x + 1)² = 25
x² + x² + 2x + 1 = 25
2x² + 2x - 24 = 0
x² + x - 12 = 0

(x + 4)*(x - 3) = 0

x1 = -4
x2 = 3

c)

x² + (x - 3)² = (x + 3)²
x² + x² -6x + 9 = x² + 6x + 9
x² . 12x = 0
x*(x - 12) = 0

x1 = 0
x2 = 12 

d)

3x² + 3 = (2x + 1)² + 4
3x² + 3 = 4x² + 4x + 1 + 4
3x² + 3 = 4x² + 4x + 5
x² + 4x + 2 = 0

d² = 16 - 8 = 8
d = 2√2

x1 = (-4 + 2√2)/2 = -2 + √2
x2 = (-4 .- 2√2)/2 = -2 - √2