Question

Calcule o valor de x .

Answer 1

$b {}^{2} = a {}^{2} + c {}^{2} - 2ac \cos( \beta ) \\ (x) {}^{2} = (5) {}^{2} + (6) {}^{2} - 2.5.6. \cos(45) \\ x {}^{2} = 25 + 36 - 60. \frac{ \sqrt{2} }{2} \\ x {}^{2} = 25 + 36 - 30 \sqrt{2} \\ x {}^{2} = 61 - 30 \sqrt{2} \\ x = \sqrt{61 - 30 \sqrt{2} } \\ ou \\ x \approx 4,31$

Answer 2

Resposta:

x=3√2-√7 ou x=3√2+√7

Explicação passo-a-passo:

Lei dos cossenos:

$\displaystyle 5^2=x^2+6^2-2(x)(6)cos45^{\circ}\\25=x^2+36-\diagup\!\!\!\!2.x.6.\frac{\sqrt{2} }{\diagup\!\!\!\!2}\\x^2-6\sqrt{2} x+36-25=0\\x^2-6\sqrt{2} x+11=0$

$\displaystyle Aplicando~a~f\'{o}rmula~de~Bhaskara~para~x^{2}-6\sqrt{2} x+11=0~~\\e~comparando~com~(a)x^{2}+(b)x+(c)=0,~temos~a=1{;}~b=-6\sqrt{2}~e~c=1\\\\\Delta=(b)^{2}-4(a)(c)=(-6\sqrt{2})^{2}-4(1)(11)=36.2-44=72-44=28\\\sqrt{\Delta}=\sqrt{28}=\sqrt{4.7}=\sqrt{4}.\sqrt{7}=2\sqrt{7}\\\\x=\frac{-(b)\pm\sqrt{\Delta}}{2(a)}=\frac{-(-6\sqrt{2})\pm2\sqrt{7}}{2(1)}=\frac{6\sqrt{2}\pm2\sqrt{7}}{2}=3\sqrt{2}\pm\sqrt{7}$