Question

 15x² -22x+8=0? resposta pfvr

Answer 1

15x²-22x+8=0

/\=(-22)²-4.15.8
/\=484-60.8
/\=484-480
/\=4

x'= -(-22)+2/30
x'=22+2/30
x'=24/30
x'=4/5

x"= -(-22)-2/30
x"=22-2/30
x"=20/30
x"=2/3

S={4/5,2/3}

Answer 2

Olá

$\boxed{\mathtt{15x^{2} - 22x + 8 = 0}}$

Usemos a fórmula de bháskara

$\boxed{\mathtt{x=\dfrac{-b\pm\sqrt{\Delta}}{2a}}}$

Substituamos os valores, sabendo que $\Delta = b^{2} - 4ac$

$\mathtt{x=\dfrac{-(-22)\pm\sqrt{(-22)^{2} - 4\cdot15\cdot8}}{2\cdot15}}$

Simplifique os valores

$\mathtt{x=\dfrac{22\pm\sqrt{484-480}}{30}}$

$\mathtt{x=\dfrac{22\pm\sqrt{4}}{30}}$

$\mathtt{x=\dfrac{22\pm2}{30}}$

Retire as raízes

$\boxed{\mathtt{x'=\dfrac{22+2}{30}~~>>~~\dfrac{24}{30}~~>>~~\dfrac{4}{5}}}$

$\boxed{\mathtt{x"=\dfrac{22-2}{30}~~>>~~\dfrac{20}{30}~~>>~~\dfrac{2}{3}}}}$ Logo, o conjunto de solução da equação é

$\boxed{\mathtt{x\in\mathbf{R}~|~S=\{\dfrac{4}{5},\dfrac{2}{3}\}}}~~\checkmark$