Question

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If x2+x=19, then what is the value of(x + 5)2 +[1/(x + 5)2] = ?
1) 77
2) 79
3) 81​

Answer 1

||✪✪ QUESTION ✪✪||

If x²+x=19, then what is the value of(x + 5)² +[1/(x + 5)²] = ?

|| ✰✰ ANSWER ✰✰ ||

Nice Question ...

Lets Solve it with very Simple method ...

Lets us assume that,

➺ (x + 5) = t

➺ x = (t - 5)

Putting this value in given data now, we get,

➪ x² + x = 19

➪ (t-5)² + (t-5) = 19

Using (a-b)² = a² + b² - 2ab now,

➪ t² + 25 - 10t + t - 5 = 19

➪ t² - 9t +20 = 19

➪ t² - 9t + 20 - 19 = 0

➪ t² - 9t + 1 = 0

Now, taking t common , we get,

➪ t(t - 9 + 1/t) = 0

➪ (t + 1/t) = 9

using (a+b)² = a² + b² + 2ab and squaring both sides we get,

➪ (t + 1/t)² = 9²

➪ t² + 1/t² + 2 * t * 1/t = 81

➪ t² + 1/t² = 81 - 2

➪ t² + 1/t² = 79 .

Now, when we put back t = (x+5) we get,

☛ (x + 5)² +[1/(x + 5)²] = 79 (Ans).

Answer 2

Question :- if x² + x = 19 , find the value of (x+5)² + 1/(x+5)² = ?

Solution :-

My Method is little bit different ,

→ x² + x = 19

→ x² = (19-x) -------- Equation (1)

Now, we have to Find (x+5)² + 1/(x+5)²

it can be written as [ (x + 5) + 1/(x+5) ] ² - 2 ( as a² + b² = (a+b)² - 2ab ) .

→ [(x+5) + 1/(x+5)]² - 2

Taking LCM now,

→ [ (x+5)² + 1 / (x+5) ]² - 2

→ [ (x² + 10x + 26) /(x+5) ]² - 2

Putting value of x² From Equation (1) now, we get,

→ [ ((19-x) + 10x + 26) /(x+5) ] ² - 2

→ [ (9x + 45) / (x+5) ]² - 2

→ [ 9(x+5) / (x+5) ] ² - 2

→ [9]² - 2

→ 81 - 2

→ 79 (Ans).