One of our brainliest, Konrad509, made this:Solve for the numeral base [tex]x[/tex] in:[tex]\frac{B_x\sqrt{74_x}}{1D_x}+J_x51_x=4G3_x[/tex].

Accepted Solution

[tex]\dfrac{B_x \sqrt{74_x}}{1D_x}+J_x51_x=4G3_x[/tex]A=10, B=11, C=12, etc.[tex]\dfrac{11\cdot x^0\cdot \sqrt{7\cdot x^1+4\cdot x^0}}{1\cdot x^1+13\cdot x^0}+19\cdot x^0\cdot (5\cdot x^1+1\cdot x^0)=4\cdot x^2+16\cdot x^1+3\cdot x^0\\\\\dfrac{11\sqrt{7x+4}}{x+13}+19(5x+1)=4x^2+16x+3\\\\\dfrac{11\sqrt{7x+4}}{x+13}+95x+19=4x^2+16x+3\\\\11\sqrt{7x+4}+95x(x+13)+19(x+13)=(4x^2+16x+3)(x+13)\\\\11\sqrt{7x+4}+95x^2+1235x+19x+247=4x^3+52x^2+16x^2+208x+3x+39\\\\11\sqrt{7x+4}=4x^3-27x^2-1043x-208\\\\121(7x+4)=(4x^3-27x^2-1043x-208)^2[/tex][tex]121(7x+4)=(4x^3-27x^2-1043x-208)^2\\\\847x+484=16 x^6 - 216 x^5 - 7615 x^4 + 54658 x^3 + 1099081 x^2 + 433888 x + 43264\\\\16 x^6 - 216 x^5 - 7615 x^4 + 54658 x^3 + 1099081 x^2 + 433041 x +42780=0[/tex]Now, the "only" thing that remains to do is solving the above equation. While making this problem I only made sure it has a solution. I didn't try to solve it myself and I didn't know it will end up with such "convoluted" polynomial. Sorry to everyone who tried to solve it... m(_ _)mI think the best way to approach it is using the rational root theorem since we know that [tex]x\in\mathbb{N}[/tex]. Moreover we can deduce that [tex]x\geq19[/tex] since there is [tex]J[/tex] and [tex]J=19[/tex].After you succesfully solve it, you should get the answer [tex]x=20[/tex].