Question

Rezolvati ecuatiile​

Answer 1

Răspuns:

Explicație pas cu pas:

a)

x^2 + 9 = 25

x^2 = 25 - 9 = 16

x = {-4; 4}

b)

169 - x^2 = 25

x^2 = 169 - 25 = 144

x = {-12; 12}

c)

x^2 + 576 = 676

x^2 = 676 - 576 = 100

x = {-10; 10}

d)

2x^2 = 288 + 162 = 450

x^2 = 450 : 2 = 225

x = {-15; 15}

e)

676 - 4x^2 = 625

4x^2 = 676 - 625 = 51

x^2 = 51/4

x = {-√51/2; √51/2}

Answer 2

$\it a)\ \ x^2+3^2=5^2 \Rightarrow x^2=5^2-3^2=(5-3)(5+3)=2\cdot6=16 \Rightarrow \\ \\ \Rightarrow \sqrt{x^2}=\sqrt{16} \Rightarrow |x|=4 \Rightarrow x=\pm4 \Rightarrow x_1=-4;\ \ x_2=4$

$\it b)\ \ 13-x^2=5^2 \Rightarrow 13^2-5^2=x^2 \Rightarrow x^2=(13-5)(13+5)=8\cdot18 \Rightarrow \\ \\ \Rightarrow x^2=414 \Rightarrow \sqrt{x^2}=\sqrt{144} \Rightarrow |x|=12 \Rightarrow x=\pm12 \Rightarrow x_1=-12,\ x_2=12$

$\it d)\ 2x^2-162=288\Big|_{:2} \Rightarrow x^2-81=144\Big|_{+81} \Rightarrow x^2=225 \Rightarrow \\ \\ \Rightarrow \sqrt{x^2}=\sqrt{225} \Rightarrow |x|=15 \Rightarrow x=\pm15 \Rightarrow x_1=-15,\ \ x_2=15$

$\it e)\ \ 25^2-5x^2=20^2 \Rightarrow 25^2-20^2=5x^2 \Rightarrow (25-20)(25+20)=5x^2 \Rightarrow \\ \\ \Rightarrow 5\cdot45=5x^2\Big|_{:5} \Rightarrow 45=x^2 \Rightarrow x^2=45 \Rightarrow \sqrt{x^2}=\sqrt{45} \Rightarrow |x|=\sqrt{9\cdot5} \Rightarrow \\ \\ \Rightarrow x=\pm3\sqrt5 \Rightarrow x_1=-3\sqrt5,\ \ x_2=3\sqrt5$