Find r if (i)<sup

(i)

42 -13r+r2=12

r2-13r+30=0

r2-10r-3r+30=0

r(r-10)-3(r-10)=0

(r-3)(r-10)=0

r= 3 or r=10

But r=10 is rejected, as in , r cannot be greater than 5.

Therefore, r=3.

(ii)

42 -13r+r2=6

r2-13r+36=0

r2-9r-4r+36=0

r(r-9)-4(r-9)=0

(r-4)(r-9)=0

r= 4 or r=9

But r=9 is rejected, as in , r cannot be greater than 5.

Therefore, r=4.

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