Question

x+(1/x+1) =5 then find the value of 6x^4(x-5) +34

Answer 1

Given: x+(1/x+1) =5

To find: the value of 6x^4(x-5) +34

Solution:

• Now we have given that x+(1/x+1) =5

• Solving this we get:

           x(x+1) + 1 = 5(x+1)

           x²+x+1 = 5x+5

           x²-4x-4=0

• Solving the equation, we get:

           { -(-4) ± √(-4)² - 4(1)(-4) }  / 2

• So, x = 2±2√2

• Putting both values in  6x^4(x-5) +34, we get:

          6(2+2√2)^4 x (2+2√2-5) + 34

          6(4+8+8√2)² x (2√2-3) + 34

          6(12+8√2)² x (2√2-3) + 34

          6x16(3+2√2)² x  (2√2-3) + 34

          6x16(9+8+12√2) x (2√2-3) + 34

          96(17+12√2) x (2√2-3) + 34

          (1632 + 1512√2) x (2√2-3) + 34

          3264√2 - 4896 + 6048 - 4536√2 + 34

          -1272√2 + 1152 + 34

          1186-1272√2

Answer:

                    So the value of x is 2+2√2 and value of the expression is 1186-1272√2.