Question

Resolva as equações do 2° grau em R (Reais) pela fórmula de Báskara:
1) 25x²=20x-4
2) 2x²= -3+7x
3) 2x=15-x²
4) 7x-12=x²

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Answer 1

Explicação passo-a-passo:

Colocar na forma normal:

1)

25x² - 20x + 4 = 0

a = 25

b = -20

c = 4

Δ=b² -4ac

Δ= (-20)²-4(25)(4)

Δ = 400-400

Δ = 0

$x={-b\pm\sqrt{\Delta} \over2a}\\ \\ x={-(-20)\pm\sqrt{0} \over2(25)}={20\over50}={2\over5}\\ \\ x'=x"={2\over5}$

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2)

2x² - 7x + 3 = 0

a = 2

b = -7

c = 3

Δ=(-7)²-4(2)(3)

Δ = 49 -24

Δ = 25

$x={-(-7)\pm\sqrt{25} \over2(2)}={7\pm5\over4}\\ \\ x'={7-5\over4}={2\over4}={1\over2}\\ \\ x"={7+5\over4}={12\over4}=3$

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3)

x² + 2x - 15=0

a=1

b=2

c= -15

Δ=2²-4(1)(-15)

Δ=4+60

Δ = 64

$x={-2\pm\sqrt{64} \over2(1)}={-2\pm8\over2}\\ \\ x'={-2-8\over2}=-{10\over2}=-5\\ \\ x"={-2+8\over2}={6\over2}=3$

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4)

x² - 7x + 12 =0

a=1

b=-7

c=12

Δ=(-7)²-4(1)(12)

Δ = 40-48

Δ = 1

$x={-(-7)\pm\sqrt{1} \over2(1)}={7\pm1\over2}\\ \\ x'={7-1\over2}={6\over2}=3\\ \\ x"={7+1\over2}={8\over2}=4$