If the sum of two numbers is 3 and the sum of their squares is 12, then their product is equal to -
A. $$\frac{3}{2}$$
B. $$\frac{2}{3}$$
C. - $$\frac{3}{2}$$
D. - $$\frac{2}{3}$$
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & {\text{a + b = 3 }}.......{\text{ (i)}} \cr & {\text{(a and b are two numbers)}} \cr & {{\text{a}}^2}{\text{ + }}{{\text{b}}^2} = 12 \cr & {\text{On squaring}}\,\,{\text{equation (i)}} \cr & {\left( {{\text{a + b}}} \right)^2} = \,{3^2} \cr & {{\text{a}}^2}{\text{ + }}{{\text{b}}^2} + 2{\text{ab}} = 9 \cr & 12 + 2{\text{ab = 9}} \cr & {\text{2ab = - 3}} \cr & {\text{ab = }}-\frac{{3}}{2} \cr} $$Related Questions on Number System
Three numbers are in ratio 1 : 2 : 3 and HCF is 12. The numbers are:
A. 12, 24, 36
B. 11, 22, 33
C. 12, 24, 32
D. 5, 10, 15
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