Question

If x-7√x -1 =0, then find the value of 2√x​

Answer 1

Step-by-step explanation:

It can be written as x2 + 7x + 1 = 0

⇒ roots of this quadratic equation are (-7 ±√45 )/2

they can be approximated as (Since √45 = 6.7)

⇒ Roots are x = – 0.15 or-6.85

Put this in x – 1/(x + 7)

Put x = - 0.15

⇒ – 0.15 – 1/(7 – 0.15)

⇒ – 0.3 and the value of 3 √5 – 7 = 3 × 2.23 – 7 = – 0.3

∴ the answer is 3√5 – 7

Formula used:

(a + b)2 = a2 + b2 + 2ab

(a - b)2 = a2 + b2 - 2ab

Calculation:

x + [1/(x + 7)] = 0

Adding both side 7

⇒ x + 7 + 1/(x + 7) = 7

Squaring both side

⇒ (x + 7)2 + 1/(x + 7)2 + 2 = 49

⇒  (x + 7)2 + 1/(x + 7)2 = 47

Subtracting both side by 2

⇒ (x + 7)2 + 1/(x + 7)2 - 2 = 47 - 2

⇒ {(x + 7) - 1/(x + 7)}2 = 45

⇒ x + 7 - 1/(x + 7) = √45

⇒ x - 1/(x + 7) = √45 - 7

∴ The value of x – [1/(x + 7)] is √45 - 7.