Question

please help me in solving the equation...
medal and fans...

Answer 1

@sourav_aich

Answer 2

Cross multiply then collect the like terms first.

Answer 3

square both sides

Answer 4

cancel the similar term in square root

Answer 5

\[9+4\lambda+12\lambda ^{2}= (3+2\lambda)^{2}\]

Answer 6

please help fully ?

Answer 7

do this for both the sides

Answer 8

what to do ?

Answer 9

could you show it ?

Answer 10

@tkhunny

Answer 11

\[ \frac{ 9+2\lambda }{(3+2\lambda )^{2/3} }= \frac{ 11+14\lambda }{(3+2\lambda )^{5/3} }\]

Answer 12

then cross multiply and keep the 3+2lambda term on one side

Answer 13

you will get a quadratic equation in lambda , solve it to get the value of lambda

Answer 14

@sourav_aich what next ?

Answer 15

the final reduced equation will be\[2\lambda ^{2} + 5\lambda + 8 = 0\]

solve it..

Answer 16

not gettt]ing right answer

Answer 17

please show u got that

Answer 18

please proceed just as i mentioned above you will get that

Answer 19

ive done that,,, not getting it

Answer 20

please redo

Answer 21

would u help ?

Answer 22

@Michele_Laino could you help ?

Answer 23

we have to compute the least common multiple between denominators. Now such least common multiple is:
\[\Large 15\sqrt {9 + 4\lambda + 12{\lambda ^2}} \]

Answer 24

so your equation is equivalent to this subsequent equation:
\[\Large 5\left( {9 + 2\lambda } \right) = 3\left( {11 + 14\lambda } \right)\]

Answer 25

furthermore, we note that the subsequent quantity
\[\Large 9 + 4\lambda + 12{\lambda ^2}\] is always positive, namely its value is always greater than zero, for any value of \lambda

Answer 26

so, we have to simplify this expression:
\[\Large 5\left( {9 + 2\lambda } \right) = 3\left( {11 + 14\lambda } \right)\]
what do you get?