Question

if m-n= 16 and m²+n²=400 then find mn​

Answer 1

Step-by-step explanation:

(m-n) 2 = 16*16

m2 + n2 -2mn = 256

400 -2mn =256

-2mn = 256-400

-2mn = -144

mn = 72

hope it helps.....

√\______Anushka❤❤

Answer 2

Given :

• m - n = 16
• m² + n² = 400

To find :

• mn

Solution :

• Using the identity : (a - b)² = a² + b² - 2ab

(m-n)² = m² + n² - 2mn

$\implies$ ( 16)² = ( m² + n²) - 2 mn

$\implies$ 256 = 400 - 2 mn

Dividing the equation by 2 .

$\tt \dfrac{256}{2} = \dfrac{400}{2} - \dfrac{2mn}{2} \\ \\ \implies \tt 128 = 200 - mn \\ \\ \implies \tt 128 - 200 = - mn \\ \\ \implies \tt - 72 = - mn \\ \\ \implies \huge \boxed{ \tt \red{mn }= \purple{ 72}}$

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$\underline{ \underline{ \large \mathfrak {\red{some} \orange{ \: important}\green{\: identities: -} }}}$

• (a+b)² = a² + b² + 2ab
• (a- b)² = a² + b² - 2ab
• a² - b² = (a + b) (a - b)
• (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
• (x + a) (x + b) = x² + (a+ b)x + ab