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## Answers

**let us take x+1/x=t**

**Then the equation becomes**

**2t²-7t+6=0**

**Byfactorization**

**2t²-4t-3t+6=0**

**Taking 2t as common in first two terms and -3 as common in next two terms**

**2t(t-2)-3(t-2)=0**

**Take t-2 as common**

**(2t-3)(t-2)=0**

**By using the principle of zer product**

**2t-3=0 or t-2=0**

**2t=3 or t=2**

**t=3/2 or t=2**

**x+1/x=2**

**x²+1/x=2**

**Multiplying both sides by x**

**x²+1=2x**

**Adding -2x on both sides**

**x²-2x+1=0**

**BY factorization**

**x²-x-x+1=0**

**Taking x as common in first two terms and -1 as common in next two terms**

**x(x-1)-1(x-1)=0**

**Take (x-1) as common**

**(x-1)²=0**

**x-1=0**

**x=1**