the sum of a number and its reciprocal is 65/8. find the number
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Let no. be x
It's reciprocal will be 1/x
x + 1/x = 65/8
(x^2+1)/x = 65/8
8( x^2 +1)=65x
8x^2+ 8=65x
8x^2+65x+8=0
8x^2+64x+x+8=0
8x(x+8)+1(x+8)=0
(8x+1)(x+8)=0
If 8x+1=0
8x=-1
x=-1/8
If x+8=0
x=-8
It's reciprocal will be 1/x
x + 1/x = 65/8
(x^2+1)/x = 65/8
8( x^2 +1)=65x
8x^2+ 8=65x
8x^2+65x+8=0
8x^2+64x+x+8=0
8x(x+8)+1(x+8)=0
(8x+1)(x+8)=0
If 8x+1=0
8x=-1
x=-1/8
If x+8=0
x=-8
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