Question

if 3^a+3^b=756 ; 7^a+2^c=375 ; 5^a+3=128.find the value of abc​

Answer 1

${3}^{a} + {3}^{b} = 756 \\ {7}^{a} + {2}^{c} = 375 \\ {5}^{a} + 3 = 128 \\ \\ now \\ {5}^{a} + 3 = 128 \\ {5}^{a} = 125 \\ {5}^{a} = {5}^{3} \\ a = 3 \\ then \\ {3}^{b} = 756 - {3}^{a} \\ {3}^{b} = 756 - {3}^{3} \\ {3}^{b} = 756 - 27 \\ {3}^{b} = 729 \\ {3}^{b} = {3}^{6} \\ b = 6 \\ also \\ {2}^{c} = 375 - {7}^{a} \\ {2}^{c} = 375 - {7}^{3} \\ {2}^{c} = 375 - 343 \\ {2}^{c} = 32 \\ {2}^{c} = {2}^{5} \\ a = 3 \\ b = 6 \\ c = 5 \\ abc = (3)(6)(5) \\ abc = 90$

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