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(a) R = 10K.Assume both diodes are conducting.We have:
100 = 10.02*I1 + 10*I2 + 0.2
 100 = 10.01*I2 + 10*I1 + 0.6
I1 = 15.692 A,I2 = -5.744 A
Solving,we find I2<0.Thus D is not ON
I1 = 9.96e+000 A and I2 = 0

(b) R=1K.Assume both diodes are ON,we have:
100 = 1.52*I1 + 1.5*I2 + 0.2
 100 = 1.515*I2 + 1.5*I1 + 0.6
Solving,we find
I1 = 39.716 A and I2 = 26.288 A.Hence assumption is valid