Find the value of x for which numbers (5x+2),(4x-1)(x+2)are in AP?????

1.	Find the value of x for which numbers (5x+2),(4x-1)(x+2)are in AP????????
Answer» Since {tex}(5x+2), (4x-1)\\ and\\ (x+2){/tex} are in AP, we have\xa0{tex}(4x-1)-(5x+2)=(x+2)-(4x-1){/tex}{tex}\\Rightarrow{/tex}\xa0{tex}4x-1-5x-2=x+2-4x+1{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}-x-3=-3x+3{/tex}{tex}\\Rightarrow{/tex}\xa02x = 6{tex}\\Rightarrow{/tex}\xa0x = 3.

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