Question

Resolva equação
A) 5× - 5²-× = 24


B) 2²× + 32 = 12.2×

Answer 1

Resposta:

5x-5²-x=24

5x-x=24+25

4x=49

x=49/4

x=12,25

2²x+32=12.2x

4x+32=24x

32=24x-4x

32=20x

x=32/20

x=8/5

Answer 2

Resposta:

A) x = 2

B) x' = 2 e x'' = 3

Explicação passo a passo:

A) $5^{x} -5^{2-x} =24$

$5^{x} -\frac{5^{2} }{5^{x} } =24$

$5^{x} -\frac{25}{5^{x} } =24$

$5^{x}.\frac{5^{x}}{5^{x}} -\frac{25}{5^{x} } =24$

$\frac{5^{x}.5^{x}}{5^{x}} -\frac{25}{5^{x} } =24$

$\frac{(5^{x})^{2} }{5^{x}} -\frac{25}{5^{x} } =24$

$\frac{(5^{x})^{2}-25}{5^{x} } =24$

$(5^{x})^{2}-25=24(5^{x})$

$(5^{x})^{2}-24(5^{x}) -25=0$

$5^{x} =\frac{-b(+/-)\sqrt{b^{2}-4ac } }{2a}$

$5^{x} =\frac{-(-24)(+/-)\sqrt{(-24)^{2}-4(1)(-25) } }{2(1)}$

$5^{x} =\frac{24(+/-)\sqrt{576-4(-25) } }{2}$

$5^{x} =\frac{24(+/-)\sqrt{576+100 } }{2}$

$5^{x} =\frac{24(+/-)\sqrt{676 } }{2}$

$5^{x} =\frac{24(+/-)\sqrt{26^{2} } }{2}$

$5^{x} =\frac{24(+/-)26 }{2}$

$5^{x} =12(+/-)13$  ← 12 – 13 = –1, Valor não pode ser negativo para qualquer potência de base positiva.

$5^{x} =12+13$

$5^{x} =25$

$5^{x} =5^{2}$

$x=2$

B) $2^{2x} +32=12.2^{x}$

$(2^{x})^{2} +32=12.2^{x}$

$(2^{x})^{2}-12.2^{x} +32=0$

$2^{x} =\frac{-b(+/-)\sqrt{b^{2}-4ac } }{2a}$

$2^{x} =\frac{-(-12)(+/-)\sqrt{(-12)^{2}-4(1)(32) } }{2(1)}$

$2^{x} =\frac{12(+/-)\sqrt{144-4(32) } }{2}$

$2^{x} =\frac{12(+/-)\sqrt{144-128 } }{2}$

$2^{x} =\frac{12(+/-)\sqrt{16 } }{2}$

$2^{x} =\frac{12(+/-)\sqrt{4^{2} } }{2}$

$2^{x} =\frac{12(+/-)4 }{2}$

$2^{x} =6(+/-)2$

$(2^{x})' =6-2$

$(2^{x})' =4$

$(2^{x})' =2^{2}$

$x' =2$

$(2^{x})'' =6+2$

$(2^{x})'' =8$

$(2^{x})'' =2^{3}$

$x'' =3$