<span>Исходное число 10х+у</span>
Обратное исходному 10у+х
<span>(10х+у) = 3ху+8
(10у+х) =2ху+5</span>
10х-3ху =8-у
<span>х(10-3у)=8-у х=(8-у)/(10-3у)</span>
10у+ (8-у)/(10-3у) = 2у(8-у)/(10-3у)+5
2у(8-у)/(10-3у)+5=10у+ (8-у)/(10-3у)
<span>2у(8-у)/(10-3у)- (8-у)/(10-3у)=10у-5 </span>
2у(8-у)- (8-у)= (10у-5)(10-3у)
<span>16у-2у</span>²<span>-8+у=100у-30у</span>²<span>-50+15у</span>
<span>28 у</span>²<span>-98х+42=0</span>
<span>4у</span>²<span>-14у+6=0</span>
<span>2у</span>²<span>-7у+3=0</span>
у = (-b ± √‾(b2 - 4ac)) / 2a=
<span>(7±
√49-4*2*3)/4=(7±√49-24)/4=(7±5)/4</span>
<span>у</span>,<span>= 3, у</span>,,<span>=1/2 не принимается</span>
х,= (8-у)/(10-3у)= 8-3/10-3*3 = 5
<span>Исходное число - 53.</span>
<span>Обратное - 35.</span>
<span>Проверка: 3ху+8= 3*3*5+8=45+8=53</span>
<span> 2ху+5=2*3*5+5=30+5=35</span>