<prompt> Seti ya pointi x,y,z ambazo ni sawa na 1,2,-5 na uhakika P hutosheleza mlingano wa fomu.10x - 4y 24z 55.Tafuta uhakika P.  <response>: Acha P a,b,c. Ikiwa pointi x,y,z ni sawa na 1,2,-5 na a,b,c, basix - 12 y - 22 z 52 x - a2 y - b2 z - c2. Kupanua, tunapatax2 - 2x 1 y2 - 4y 4 z2 10z 25 x2 - 2ax a2 y2 - 2by b2 z2 - 2cz c2,ambayo hurahisisha2a - 2 x 2b - 4 y 2c 10 z a2 b2 c2 - 30.Tunataka hili liendane na mlingano10x - 4y 24z 55.Tukiweka 2a - 2 10, 2b - 4 -4, na 2c 10 24, basi a 6, b 0, na c 7. Kumbuka kuwa a2 b2 c2 - 30 55, ili thamani hizi zifanye kazi. Hivyo, a,b,c 6,0,7. 