Question

Sa se determine valorile reale ale nr a stiind ca distanta dintree punctele A(3,2) si B(a,8) este egala cu 8. va roooog

Answer 1

[tex]AB= \sqrt{(x_{B}- x_{A})^2+(} y_{B}- y_{A})^2 AB= \sqrt{(a-3)^2+(8-2)^2}= \sqrt{a^2-6a+9+36}= \sqrt{a^2-6a+45} [/tex]


$\sqrt{a^2-6a+45} =8$

Ridicam la patrat ambii membri


[tex](\sqrt{a^2-6a+45})^2=(8)^2 a^2-6a+45=64 a^2-6a+45-64=0 a^2-6a-19=0[/tex]

[tex]a=1 b=-6 c=-19 delta=b^2-4ac delta=(-6)^2-4*1*(-19)=36+76=112 [/tex]

[tex]x1= \frac{6+4 \sqrt{7} }{2}= \frac{2(3+2 \sqrt{7}) }{2}=3+2 \sqrt{7} x2=3-2 \sqrt{7} [/tex]