Question

Given m² + n² =546 and mn = 88,find the value of m and n?

Answer 1

Answer:

$m + n = \sqrt{722}$

Step-by-step explanation:

$m^{2} + n^{2} = 546$

$(m + n)^{2} -2mn = 546$                         using[  $a^{2} + b^{2} = (a + b)^{2} - 2ab$ ]

$(m + n)^{2} - 2(88) = 546$

$(m + n)^{2} =546 + 176$

$(m + n)^{2} = 722$

$m + n = \sqrt{722}$

Answer 2

Sᴏʟᴜᴛɪᴏɴ :-

→ m² + n² = 546

Adding 2mn both sides ,

→ m² + n² + 2mn = 546 + 2mn

using a² + b² + 2ab = (a + b)² in LHS,

→ (m + n)² = 546 + 2mn

Putting value of mn = 88 in RHS now,

→ (m + n)² = 546 + 2*88

→ (m + n)² = 546 + 176

→ (m + n)² = 722

Square - Root both sides now,

→ m + n = √722 = 19√2

Now,

→ m² + n² = 546

Subtracting 2mn both sides ,

→ m² + n² - 2mn = 546 - 2mn

using a² + b² - 2ab = (a - b)² in LHS,

→ (m - n)² = 546 - 2mn

Putting value of mn = 88 in RHS now,

→ (m - n)² = 546 - 2*88

→ (m - n)² = 546 - 176

→ (m - n)² = 370

Square - Root both sides now,

→ m - n = √370

conclusion :- Real values of m and n are not Possible. or , m and n not belongs to real numbers .