Question

x^3-17x^2-x-7/x^2+6x-7​

Answer 1

Answer:

54 will be the answer to your question

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Answer 2

Answer:

$</p><p>Given equation, x </p><p>5</p><p> −6x </p><p>4</p><p> −17x </p><p>3</p><p> +17x </p><p>2</p><p> +6x−1=0</p><p></p><p>Consider f(x) =x </p><p>5</p><p> −6x </p><p>4</p><p> −17x </p><p>3</p><p> +17x </p><p>2</p><p> +6x−1</p><p></p><p>Notice that this is a reciprocal equation of odd degree which has the opposite signs of the first and last term.</p><p></p><p>∴(x−1) is one factor of the given equation and the quotient is another reciprocal function which has same signs of the first and last term.</p><p></p><p>∴f(x)=(x−1)(Ax </p><p>4</p><p> +Bx </p><p>3</p><p> +Cx </p><p>2</p><p> +Bx+A)</p><p></p><p>Comparing the coefficient, we have A=1,B=−5,C=−22</p><p></p><p>⟹f(x)=(x−1)(x </p><p>4</p><p> −5x </p><p>3</p><p> −22x </p><p>2</p><p> −5x+1)</p><p></p><p>Consider g(x)=x </p><p>4</p><p> −5x </p><p>3</p><p> −22x </p><p>2</p><p> −5x+1=(x </p><p>4</p><p> +1)−5(x </p><p>3</p><p> +x)–22x </p><p>2</p><p> </p><p></p><p>We need to find the roots of g(x)=0</p><p></p><p>⟹(x </p><p>2</p><p> +x </p><p>−2</p><p> )–5(x+x </p><p>−1</p><p> )–22=0[dividing byx </p><p>2</p><p> ]</p><p></p><p>Substitute x+x </p><p>−1</p><p> =y in the above equation</p><p></p><p>⟹(y </p><p>2</p><p> −2)−5y−22=0⟹y </p><p>2</p><p> −5y−24=0⟹(y−8)(y+3)=0</p><p></p><p>∴x+x </p><p>−1</p><p> =8 and x+x </p><p>−1</p><p> =3</p><p></p><p>Solving the first quadratic equations we have, x=4± </p><p>15</p><p> </p><p> </p><p></p><p>Solving the second quadratic equations we have, x= </p><p>2</p><p>3± </p><p>5</p><p> </p><p> </p><p> </p><p> </p><p></p><p>∴ roots of the given equation are 1,4± </p><p>15</p><p> </p><p> , </p><p>2</p><p>3± </p><p>5$

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