Question

If 3x=2+5i then find the value of 27x³-36x²+87x-5 is

Answer 1

Answer:

345

Step-by-step explanation:

x=2+5/3

=7/3

27×(7/3)^3 -36×(7/3)^2+87×7/3 -5

27×343/27 -36×49/9 +29×7 -5

343 -196 +203 -5

546 -201

345

Answer 2

Answer:

The value of the expression is 160i-5

Step-by-step explanation:

We know the values of i³ = -i

                                       i² = -1

(a + b)³ = a³ + b³ + 3ab(a + b)

(a + b)² = a² + b² + 2ab.

Given that 3x = 2+5i

⇒ x = (2+5i)/3

We have to find the value of

27x³-36x²+87x-5    -------(1)

Given x value is

x= (2+5i)/3

Put this x value in equation(1)

then,

$27x^{3} -36x^{2} +87x-5$

=$27(\frac{2+5i}{3} )^{3} -36(\frac{2+5i}{3} )^{2} +87(\frac{2+5i}{3})-5$

Simplify the above expression

$27(\frac{2^{3} +(5i)^{3}+3(2)(5i)(2+5i) }{27} )-36(\frac{2^{2}+(5i)^{2}+2(2)(5i) }{9} )+87(\frac{2+5i}{3} )-5\\=8+125i^{3} +30i(2+5i)-4(4+25i^{2}+20i)+29(2+5i)-5$

We know that i³= i , i² = -1

put these values in above expression

$=8-125i+60i+150i^{2} -16-100i^{2} -80i+58+145i-5\\=8-150+100-16+58-5-125i+60i-80i+145i\\=166-171+285i-125i\\=-5+160i$

Therefore, the value of the expression is 160i-5

that is, 5(32i-1).