Question

1) যদি m+n =5 এবং mn =6 হয়, তাহলে
$(m {}^{2} + n^{2} )(m {}^{3} + n {}^{3} )$
কত​

Answer 1

Question:—

যদি m+n =5 এবং mn =6 হয়, তাহলে

${(m {}^{2} + n^{2} )(m {}^{3} + n {}^{3} )}$কত ?

$\huge\underline{\overline{\mid\star{\frak{\red{♣ Solution ♣:→}}\star\mid}}}$

Given,

• m+n → 5
• mn → 6

→ So,

$\bold{( {m}^{2} + {n}^{2} )( {m}^{3} + {n}^{3} )}$

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

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

$= ({(m + n)}^{2} - 2mn )(m + n)( {(m + n)}^{2} -3 mn )$

$= ( {5}^{2} - 2 \times 6)(5)( {5}^{2} - 3 \times 6)$

$= (25 - 12) \times 5 \times (25 - 18)$

$= 13 \times 5 \times 7$

$= \bold{455}$

Formula used :—

$\large \boxed{ \bold{★ \: {x}^{2} + {y}^{2} = {(x + y)}^{2} - 2xy}}$

$\large \boxed{ \bold{★ \: {x}^{3} + {y}^{3} = {(x + y)( {x}^{2} - xy + {y}^{2} ) }}}$