EXERCISE (S-1) 1. Let A denotes the...
Question

# EXERCISE (S-1) 1. Let A denotes the value of logio ( ab + ab)- 4(a+b) ab-J(ab)2 - 4(a+b) It log10) when a = 43 and b = 57 and B denotes the value of the expression (218018).(31%). Find the value of (A.B).

JEE/Engineering Exams
Maths
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( A=log _{10}left(frac{a b+sqrt{(a b)^{2}-4(a+b)})}{+log _{10}left(frac{a b-sqrt{(a b)^{2}-4(a+b)}}{2}right)}right. ) ( begin{aligned} &=log _{10}left(frac{left.a^{2} b^{2}-(a b)^{2}-4(a+b)right)}{4}right) =& log _{10}left(frac{4(a+b)}{4}right)=log _{10}(a+b) =& log _{10}(43+57)=log _{10}(100) =& log _{10}(10)^{2}=2 log _{10} 10 =& 2^{log _{6} 18} cdot 3^{log _{6} 3} =& 2 frac{log left(2 times 3^{2}right)}{2(28(2 times 3)} cdot 3^{frac{log 3}{log (2 times 3)}} =& 2^{frac{log 2+2 log 3}{192+log 3}} frac{193}{log 2+log 3} end{aligned} ) ( =2 ) ( 1+frac{log 3}{log 2+log 3} cdot frac{log 3}{3^{log 2}+log 3} ) ( =2 int_{log _{6} 3}^{(j)^{2}}=2 cdot 2^{frac{log 3}{2} cdot 6} cdot 3^{frac{cot 3}{46}} ) ( =2 cdot 6^{frac{1}{6}}=2 cdot 3 ) ( A+B=2+6=8 )