Question

( x + 1 upon x) find its value if x+ 1upon x= 4

Answer 1

I think I must find the value of x

x + 1/x = 4

x²+1/x = 4

cross multiplication

x²+1=4x

x²- 4x + 1 =0

it is in a form of ax² + bx + c = 0

a = 1 ,b = - 4 ,c = 1

by using Shridhar's law

$= x \ \\ = \: - b + - \sqrt{b {}^{2} - 4ac } \div2a \\ = - ( - 4) + - \sqrt{( - 4){}^{2} -4(1)(1) } \div 2(1) \\ = \: 4 + - \sqrt{12} \div 2 \\ = \: 4 \: + - 2 \sqrt{3} \div 2 \\ \\ x \: = \: 4 + 2 \sqrt{3} \div 2 \\ x = 2(2 + \sqrt{3} ) \div 2 \\ \:x = \: 2 + \sqrt{3 } \: \: or \\ \\ x \: = 4 - 2 \sqrt{3} \div 2 \\ x \: = \: 2(2 - \sqrt{3} ) \div 2 \\ x \: = \: 2 - \sqrt{3}$