Question

Q1)) If x = 2 then the value of x3 + 27x2 + 243x + 631 is
A)1211
B)1231
C)1233
D)1321


step by step explain​

Answer 1

Question :-

i) If x = 2, then the value of x³ + 27x² + 243x + 631 is

a)1211 b) 1231 c) 1233 d) 1321

Answer :-

Given :

• The value of x is 2.

To find :

• The value of x³ + 27x² + 243x + 631.

Solution :

Let's put the value of x in the given equation,

= (2)³ + 27(2)² + 243 × 2 + 631

= 8 + 27 × 4 + 486 + 631

= 8 + 108 + 486 + 631

= 1233

Hence, the given option (c) 1231 is the correct answer.

More formulas :-

• (a + b)² = a² + b² + 2ab
• (a - b)² = a² + b² - 2ab
• (a +b)³ = a³ + b³ + 3ab(a + b)
• (a - b)³ = a³ - b³ - 3ab(a - b)
• (a - b)² = (a + b)² - 2ab
• (a + b)² = (a - b)² + 2ab

Answer 2

Given that , We've provided with the Value of x is 2 .

Exigency To Find : The value of x³ - 27x² + 243x + 631 ?

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$\qquad:\implies \sf \: x^3 + 27x^2 + 243x + 631 \:\:$

$\qquad \dag\:\underline {\frak{ By\;,\:Putting \:the \:Given \: value \:of \: \pmb{\frak{ x }}\:\::}}$

$\qquad:\implies \sf \: x^3 + 27x^2 + 243x + 631 \:\:\\\\ \\ \qquad:\implies \sf \: (2)^3 + 27(2)^2 + 243(2) + 631 \:\:\\\\\\ \qquad:\implies \sf \: 8 + 27(2)^2 + 243(2) + 631 \:\:\\\\\\ \qquad:\implies \sf \: 8 + 27(4) + 243(2) + 631 \:\:\\\\ \\ \qquad:\implies \sf \: 8 + 108 + 243(2) + 631 \:\:\\\\\\ \qquad:\implies \sf \: 8 + 108 + 486 + 631 \:\:\\\\\\ \qquad:\implies \sf \: 116 + 486 + 631 \:\:\\\\\\\qquad:\implies \sf \: 602 + 631 \:\:\\\\\\ \qquad:\implies \sf \: 1233 \:\:\\\\\\ \qquad:\implies \underline {\boxed {\pmb{\frak{ \: x^3 + 27x^2 + 243x + 631 \:\:=\:\:1233 \:\:}}}}\:\:\bigstar \:\:$

$\qquad \therefore \:\:\underline {\sf Hence, \:The \:Value \:of \:x^3 + 27x^2 + 243x + 631 \:is\:\:\:\pmb{\bf Option \:C \:) \:1233\:}\:\:.\:}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

$\qquad \qquad \underline {\bigstar\pmb{\mathbb{ ADDITIONAL \:\:INFORMATION \::\:}}}\:$

$\dag \:\:\underline { \underline {\purple{\sf Algebraic \; Indentity \:\:-\: }}}$

$\qquad \sf ( I ) \:\:( a + b)^2 =\:a^2 + b^2 + 2ab \:$

$\qquad \sf ( II ) \:\:( a - b)^2 =\:a^2 + b^2 - 2ab \:$

$\qquad \sf ( III ) \:\: a^2 - b^2 =\:( a + b ) ( a - b ) \:$

$\qquad \sf ( IV ) \:\:( x + b ) ( x + b ) \:=\:x^2 + ( a + b ) x + ab \:$

$\qquad \sf ( V ) \:\: ( a + b + c )^2\:=\: a^2 + b^2 + c^2 + 2ab + 2bc + 2ca \: \:$$\qquad \sf ( VI ) \:\: ( a + b )^3\:=\: a^3 + b^3 + 3ab ( a + b ) \: \:$

$\qquad \sf ( VII ) \:\: ( a - b )^3\:=\: a^3 - b^3 - 3ab ( a - b ) \: \:$

$\qquad \sf ( VIII ) \:\: a^3 + b^3 + c^3 - 3abc\:=\: ( a + b + c ) \: ( a^2 + b^2 + c^2 - ab - bc - ca ) \: \:$