Question

Solve it............!!!!!!!!!!​

Answer 1

$\sf{\huge{\mathfrak{\pink{\underline{Question}}}}}$

• Find the coefficient of x2 in the expansion of

$( x^2 + x + 1 )^2 + ( x^2 - x + 1 )^2$

$\sf{\huge{\mathfrak{\pink{\underline{Solution}}}}}$

• evaluate the equation first

$\sf\implies( x^2 + x + 1 )^2 + ( x^2 - x + 1 )^2$

$\sf{\bold{\red{\boxed{( a + b + c)^2= a^2 + b^2 + c^2 + 2ab + 2bc + 2ca}}}}$

$\sf\implies ( {x^2}^2 + x^2 + 1^2 + 2(x^2)(x) + 2(x)(1) + 2(1)(x^2) )$

$+ ( {x^2}^2 + x^2 + 1^2 + 2(x^2)(-x) + 2(-x)(1) + 2(1)(x^2) )$

$\sf\implies x^4 + x^2 + 1 +\cancel{ 2x^3} +\cancel{ 2x} + 2x^2 + x^4 + x^2 + 1 \cancel{- 2x^3}\cancel{- 2x }+ 2x^2$

$\sf\implies x^4 + x^2 + 1 + 2x^2 + x^4 + x^2 + 2x^2$

$\sf\implies 2x^4 + 6x^2 + 1$

• coefficient of $x^2$

$\sf\implies + 6$

$\sf{\underline{\boxed{\mathfrak{\purple{\dag + 6}}}}}$

_______________❤

Answer 2

$\bf {\underline {\underline{✤QƲЄƧƬƖƠƝ}}}$

Find the coefficient of x²

$\bf{ {( {x}^{2} + x + 1)}^{2} } + {( {x}^{2} - x + 1)}^{2}$

$\bf  {\underline {\underline{✤ ƛƝƧƜЄƦ}}}$

Coefficient of x² is +6

$\bf {\underline {\underline{✤ƬƠ \: \: ƇƛLƇƲLƛƬЄ}}}$

• Coefficient of x²

$\bf {\underline {\underline{✤ SƠԼƲƬƖƠƝ}}}$

$\bf{ {( {x}^{2} + x + 1)}^{2} } + {( {x}^{2} - x + 1)}^{2}$

Formula :-

$\bf \purple{ {(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ca}$

$\bf{ {x}^{4} + {x}^{2} + 1 + {2x}^{3} + {2x}^{2} + 2x + { ( {x}^{2} - x + 1)}^{2} }$

$\bf{ {x}^{4} + {x}^{2} + 1 + {2x}^{3} + {2x}^{2} + 2x + {x}^{4} + {x}^{2} + 1 - {2x}^{3} + {2x}^{2} - 2x}$

$\bf{ {x}^{4} + {x}^{2} + 1 + { \cancel{2x}^{3}} + {2x}^{2} + 2x + {x}^{4} + {x}^{2} + 1 {\cancel { - 2x}^{3} } + {2x}^{2} - 2x}$

$\bf{ {x}^{4} + {x}^{2} + 1 + {2x}^{2} +{ \cancel {2x}} + {x}^{4} + {x}^{2} + 1 + {2x}^{2} - { \cancel{2x}}}$

$\bf{ \pink{{x}^{4} }+ {x}^{2} + 1 + {2x}^{2} + \pink{ {x}^{4} }+ {x}^{2} + 1 + {2x}^{2} }$

$\bf{ {2x}^{4} + \pink{ {x}^{2} }+ 1 + \pink{ {2x}^{2} } + \pink{ {x}^{2} }+ 1 + \pink{{2x}^{2}} }$

$\bf{ {2x}^{4} + {6x}^{2} + \pink{1} + \pink{1}}$

$\bf{ {2x}^{4} + {6x}^{2} + 2}$

Therefore, Coefficient of x² is +6.

$\bf \pink{hope \: } \purple{it \: } \blue{helps \: } \red{uh..}$