# CAT 2017 Question Paper | Quants Slot 1

###### CAT Previous Year Paper | CAT Algebra Questions | Question 22

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Question 22 : If x + 1 = x2 and x > 0, then 2x4 is :

1. 6 + 4√5
2. 3 + 5√5
3. 5 + 3√5
4. 7 + 3√5

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### Explanatory Answer

##### Method of solving this CAT Question from Algebra

Given that x + 1 = x2 and x > 0 then we have to find the value of 2x4.
This 2x4 can be found by either finding x first so let us take,
⟹ x + 1 = x2
⟹ x2 - x – 1 = 0
⟹ x2 - x + $$frac{1}{4}$ = 1 + $\frac{1}{4}$ ⟹$x - $$frac{1}{2}$)2 = $\frac{5}{4}$ ⟹ x - $\frac{1}{2}$ = ± $\frac{√5}{2}$ ⟹ x = $\frac{1}{2}$ ± $\frac{√5}{2}$ ⟹ x + 1 = x2 ⟹$x + 1)2 = (x2)2
⟹ x2 + 2x + 1 = x4
⟹ x + 1 + 2x + 1 = x4
⟹ 3x + 2 = x4
⟹ 6x + 4 = 2x4
We have already found the value of x = $$frac{1}{2}$ ± $\frac{√5}{2}$, so we can substitute that in place of x. We will get, ⟹ 6$$$frac{1 + √5}{2}$) + 4 = 2x4 ⟹ 3 + 3√5 + 4 = 2x4 ⟹ 7 + 3√5 = 2x4 Hence if x + 1 = x2 and x > 0, then 2x4 is equal to 7 + 3√5. Key thing here is to somehow find x, and then write x4 in terms of x and then find the value of 2x4 The question is "If x + 1 = x2 and x > 0, then 2x4 is :" ##### Hence, the answer is 7 + 3√5 Choice D is the correct answer ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2021Enroll at 49,000/- 44,000/- Online Classroom Batches Starting Now! ###### Best CAT Coaching in Chennai Introductory offer of 5000/- Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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