Question

The product of m and n if difference between then is 16 and sum of their squares is 400 is

Answer 1

ATTACHMENT................⛄
MARK BRAINLIEST

Answer 2

The product of mn is 71.9556.

Step-by-step explanation:

Given : The difference between m and n is 16 and sum of their squares is 400.

To find : The product of m and n ?

Solution :

The difference between m and n is 16.

i.e. $m-n=16$ ...(1)

Sum of their squares is 400.

i.e. $m^2+n^2=400$ .....(2)

Substitute m value from (1) in (2),

$(16+n)^2+n^2=400$

$256+n^2+32n+n^2=400$

$2n^2+32n-144=0$

$n^2+16n-72=0$

Solving by quadratic formula, $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Here, a=1, b=16 and c=-72

$n=\frac{-16\pm\sqrt{16^2-4(1)(-72)}}{2(1)}$

$n=\frac{-16+\sqrt{544}}{2},\frac{-16-\sqrt{544}}{2}$

$n=3.66,-19.66$

Substitute in (1),

When n=3.66,

$m-3.66=16$

$m=19.66$

The product of m and n is $mn=(19.66)(3.66)=71.9556$

When n=-19.66,

$m-(-19.66)=16$

$m=-3.66$

The product of m and n is $mn=(-3.66)(-19.66)=71.9556$

Therefore, the product of mn is 71.9556.

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