Let maximum value of the expression y=|k-3| 2 x+|t-4| 2 x+3 where 0 k 6 and 1 t 7 is equal to 6 then find the minimum value of (k^2+t^2 ) .

Step-by-step solution

aligned .y |_ . & = (k-3)^2+(t-4)^2 +3=6 (k-3)^2+(t-4)^2 & =9 aligned Put k-3=3 Put t+4=3 aligned k^2+t^2 & =(3+3 )^2+(-4+3 )^2 & =34+18 -24 + .t^2 |_ . & =(34-30)=4 aligned k^2+ .t^2 |_ . =(34-30)=4