Two fractions are such that their product is -4 and sum is $$\frac{{ - 32}}{{15}}.$$ Find the two fractions.
A. $$\frac{6}{{15}},\,\frac{{ - 10}}{3}$$
B. $$\frac{6}{5},\,\frac{{ - 10}}{3}$$
C. $$\frac{7}{2},\,\frac{{ - 8}}{7}$$
D. $$\frac{{ - 10}}{7},\,\frac{{14}}{5}$$
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & {\text{Let the fractions }}a{\text{ and }}b \cr & ab = - 4 \cr & a + b = \frac{{ - 32}}{{15}}{\text{ }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}\left( 1 \right) \cr & {\left( {a + b} \right)^2} = {\left( {a - b} \right)^2} + 4ab \cr & {\left( {\frac{{ - 32}}{{15}}} \right)^2} = {\left( {a - b} \right)^2} + 4\left( { - 4} \right) \cr & {\left( {a - b} \right)^2} = \frac{{1024}}{{225}} + 16 \cr & a - b = \sqrt {\frac{{4624}}{{225}}} \cr & a - b = \frac{{68}}{{15}}{\text{ }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}\left( 2 \right) \cr & {\text{Equate equation }}\left( 1 \right){\text{ and }}\left( 2 \right){\text{,}}\,{\text{we get}} \cr & a = \frac{{18}}{{15}} = \frac{6}{5} \cr & b = \frac{{ - 100}}{{30}} = \frac{{ - 10}}{3} \cr} $$Related Questions on Simplification
A. 20
B. 80
C. 100
D. 200
E. None of these
A. Rs. 3500
B. Rs. 3750
C. Rs. 3840
D. Rs. 3900
E. None of these
Join The Discussion