If x2+y2+2x+1=0 then the value of x31+y35 ?????
D Debasish New member Joined Jan 19, 2012 Messages 13 Jan 20, 2012 #1 If x2+y2+2x+1=0 then the value of x31+y35 ?????
R rexmorgan New member Joined Jan 14, 2012 Messages 13 Jan 20, 2012 #2 Need a little more info to help you out.
S soroban Elite Member Joined Jan 28, 2005 Messages 5,586 Jan 20, 2012 #3 Hello, Debasish! If x2+y2+2x+1 = 0\displaystyle \text{If }x^2+y^2+2x+1\,=\,0If x2+y2+2x+1=0 . . find the value of: x31+y35\displaystyle \text{find the value of: }\:x^{31}+y^{35}find the value of: x31+y35 Click to expand... We have: .x2+2x+1+y2 = 0⇒(x+1)2+y2 = 0\displaystyle x^2+2x+1 + y^2 \:=\:0 \quad\Rightarrow\quad (x+1)^2 + y^2 \:=\:0x2+2x+1+y2=0⇒(x+1)2+y2=0 . . Hence: .x=-1, y=0\displaystyle x = \text{-}1,\:y = 0x=-1,y=0 Therefore: .x31+y35 = (-1)31+(0)35 = −1+0 = −1\displaystyle x^{31} + y^{35} \;=\;(\text{-}1)^{31} + (0)^{35} \;=\;-1 + 0 \;=\;-1x31+y35=(-1)31+(0)35=−1+0=−1
Hello, Debasish! If x2+y2+2x+1 = 0\displaystyle \text{If }x^2+y^2+2x+1\,=\,0If x2+y2+2x+1=0 . . find the value of: x31+y35\displaystyle \text{find the value of: }\:x^{31}+y^{35}find the value of: x31+y35 Click to expand... We have: .x2+2x+1+y2 = 0⇒(x+1)2+y2 = 0\displaystyle x^2+2x+1 + y^2 \:=\:0 \quad\Rightarrow\quad (x+1)^2 + y^2 \:=\:0x2+2x+1+y2=0⇒(x+1)2+y2=0 . . Hence: .x=-1, y=0\displaystyle x = \text{-}1,\:y = 0x=-1,y=0 Therefore: .x31+y35 = (-1)31+(0)35 = −1+0 = −1\displaystyle x^{31} + y^{35} \;=\;(\text{-}1)^{31} + (0)^{35} \;=\;-1 + 0 \;=\;-1x31+y35=(-1)31+(0)35=−1+0=−1
D Deleted member 4993 Guest Jan 20, 2012 #4 I want to add a little explanation to Soroban's elegant solution. (x+1)2 and y2 will be always positive - because those are square numbers. Sum of two positive numbers can be equal to zero - iff each number is equal zero. Then rest of the story....
I want to add a little explanation to Soroban's elegant solution. (x+1)2 and y2 will be always positive - because those are square numbers. Sum of two positive numbers can be equal to zero - iff each number is equal zero. Then rest of the story....
