Question

(x-1)³+(x-2)³+(x-3)³+(x-4)³+(x-5)³=0​

Answer 1

Answer:

Solution is x1=3,x2=3+2.45i,x3=3-2.45i

Step-by-step explanation:

In the Given Question power of x is 3

we know

the Equation is (x-1)³+(x-2)³+(x-3)³+(x-4)³+(x-5)³=0​

$(A+B)^{2} =(A+B)(A+B)\\\\(A+B)^{3} =(A+B)(A+B)(A+B)\\\\also we know (A-B)^{3}=x^{3} -y^{3} -3x^{2} y+3xy^{2}$

the Equation is (x-1)³+(x-2)³+(x-3)³+(x-4)³+(x-5)³=0​

$(x^{3}-1-3x^{2}+3x) +(x^{3}-8-6x^{2}+12x)+(x^{3}-27-9x^{2}+27x)+(x^{3}-64-12x^{2}+48x)+(x^{3}-125-15x^{2}+75x)\\5x^{3}-225-45x^{2}+165x =0\\5x^{3}-45x^{2}+165x-225=0\ x1=3,x2=3+2.45i,x3=3-2.45i$