To find the value of k that makes the expression x^4 - 2x + k a perfect square, apply the algebraic identity (a - b)^2 = a^2 + b^2 - 2ab by setting a = x^2 and b = 1, which transforms the expression into (x^2 - 1)^2 = x^4 + 1 - 2x. Comparing this with the original expression x^4 - 2x + k, we determine that k must equal 1 for the expression to be a perfect square.
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Maths and Reasoning class for competitive aspirantsAdded:
Hi friends, welcomes to a new class.
So here different type of question have been put to boost your knowledge especially math reasoning. See here the first question the question has been given here as x to the^ 4 - 2 * x + k. We have to find out the value of k. So how we can find out the value of K?
Please try and give the answer. So this is a tricky one and you have to use the logic which is very important to solve this question.
So we can use here the logic and also formula to solve this question. So my concern is that you will solve this problem by using formula. So this is the hints. So use the formula and after that you will able to get the answer.
So he has been given x ^ 4 - 2x + and k = question mark. So what will be the value of k? Please try and give the answer.
So which logic will be used here to solve this problem?
Please give the answer.
So friends here has been given x ^ 4 - 2x + k k equal to question mark.
So here which value will be the k? So what value will be the k? Okay. So we have to put the value of k so that uh it will be a perfect All right.
So friends here so see the solution.
So here x ^ 4 - 2 x s² + k.
So we know that a minus b.
So a minus b² = a² + b² - 2 a b. So now we can rewrite x ^ 4 as 2 s² the power 4 to the power 2 - 2 s² + k.
So see here friends as a will be s² and b will be minus1. So by using this formula we can determine that a = x² and b = - 1. So here k so here 1 minus k² = k so k = 1. So the value of K will be one.
So friends see here here + 2 here + 5 + 10 and + 17.
and see here + 3 + 5 + 7 after that will be + 9. Okay. So 17 + 9 = 16. So 37 + 16 So 37 + 16 = to So friends, so 63 will be the correct answer.
So friends see here the question has been given here as a square + b a square + c a square minus a b minus b c minus c a and zero equal to zero and we have to find out a b² and c. So to solve like this questions and we have to equalize both sides and after that we will able to get the answer. Okay. So see here in which way the problem can be solved. So first of all we have to equalize both sides as he has been given zero. So uh the value of a a b and c will be put here to equalize both sides. So if there is zero and uh there will be also zero. So see here. So if we take a so so if we take a = 1 and b = on 1 and c = on 1. So then both sides will be equal. So see here on square on square + on square + on square minus on time on minus on time on minus on time on equal to 0. So see here so here 3 - 3 equal to 0. So 0 equal to 0. So both sides are equal. So that is why the answer will be a is 1 is to 1 is to 1. So a to b is to c will be 1 is to 1 is to 1. So this will be the answer.
Okay.
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