Math, asked by rudresh200703, 3 months ago

If x = 2 + √3 the value of x3 + 3x2 – 27 x + 87 is

Answers

Answered by Anonymous
9

____________________________

____________________________

{\underline{\bf{Given,}}}

\small{\leadsto\sf{x =  2 + \sqrt{3}}}

\small{\leadsto\sf{p(x)=x^{3}+3x^{2}-27x+87}}

{\underline{\bf{To \:find,}}}

the value of \small{\sf{p(x)=x^{3} + 3x^{2} - 27x + 87}}

{\underline{\bf{Solution,}}}

Putting, x = 2 + √3 in p(x) = x³+ 3x² - 27x + 87

\dashrightarrow (2 + √3)³ + 3(2 + √3)² - 27(2 + √3) + 87

\dashrightarrow(2)³ + (√3)³ + 3(2)(√3)(2 + √3) + 3(2 + √3)² - 27(2 + √3) + 87

\dashrightarrow4 + 3√3 + 6√3( 2 + √3) + 3{(2)²+ (√3)²+2(2)(√3)} - 54 - 27√3 + 87

\dashrightarrow4 + 3√3 + 12√3 + 54 + 3(4 + 3 + 4√3) - 27√3 + 33

\dashrightarrow4 + 3√3 + 12√3 + 54 + 12 + 9 + 12√3 - 27√3 + 33

\dashrightarrow3√3 + 12√3 + 12√3 - 27√3 + 4 + 54 + 12 + 9 + 33

\dashrightarrow \cancel{24\sqrt{3}}\cancel{-24\sqrt{3}} + 112

\dashrightarrow112

\therefore{\boxed{\sf{\pink{p(x)=x^{3}+3x^{2}-27x+87=112}}}}

____________________________

____________________________

Identities used:-

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

____________________________

____________________________

Similar questions