Question

l^2+m^2=13 or l+m =5 . lm =?​

Answer 1

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Answer 2

Answer:

lm = 6

Step-by-step explanation:

Given equations-

$l^{2}+m^{2} = 13$          ------------------------ 1

l + m = 5                   -------------------------  2

From equation 2

l + m = 5

l = 5 - m

Put l = 5 - m in equation 1

We have- $l^{2}+m^{2} = 13$

$(5-m)^{2}+m^{2} = 13$

Using formula-

$(a-b)^{2} = a^{2} -2ab + b^{2}$

$5^{2} - 2*5*m + m^{2} + m^{2} = 13$

$25 - 10m + 2m^{2} = 13$

$2m^{2}-10m+25-13=0$

$2m^{2}-10m+12=0$

$2m^{2}-6m-4m+12=0$

$2m(m-3) -4(m-3) = 0$

$(m-3)(2m-4) = 0$

If (m-3) = 0            

Then m = 3  

 If (2m - 4) = 0

Then 2m = 4

m = 2          

Put m = 2 in equation 2-

l + m = 5

l + 2 = 5

l = 5 - 2

l = 3

So,

lm = 3 × 2

lm = 6

Put m = 3 in equation 2-

l + m = 5

l + 3 = 5

l = 5 - 3

l = 2

So,

lm = 2 × 3

lm = 6