Simple and Mindblowing Technique to Crack This Math Challenge

Added: 2026-05-25

[00:00:02]Welcome to Infigan my dear friends.

[00:00:04]Today in this video we'll be solving one very very interesting question from algebraic expressions. Here we have x = <unk>3 + 1 / 2. Then it is said to find the value of 16 x^ 4 - 16xq - 12x² + 12 x + 5.

[00:00:25]So let's get started by writing here required expression is e.

[00:00:32]Now we will write x = <unk>3 + 1 / 2.

[00:00:43]Now we will cross multiply and we can write 2x will be equal to <unk>3 + 1.

[00:00:56]Now we are going to subtract 1 from both the sides to get square root 3 in the rhs. So we will cancel plus and minus one.

[00:01:08]So we can write here 2x - 1 will be equal to square <unk>3.

[00:01:17]Now we'll be squaring both sides. We'll put two in LHS. So part two in RHS.

[00:01:26]Now square root and square will be cancelled out from right hand side.

[00:01:33]Now in LHS we will be applying a minus b whole square identity.

[00:01:39]So if I will write here a - b whole² formula then equal to a² - a b + b².

[00:01:54]So let's apply. We'll write here 4x² - 4x + 1 in LHS and 3 in the RS.

[00:02:12]Let me write here 4x² - 4x + 1 = 3.

[00:02:24]Now we will take + 1 to the RS and we can write 4x² - 4x = 3 - 1 which will be equal to 2.

[00:02:43]Now we will divide both sides by four.

[00:02:46]So let us divide by four.

[00:02:50]We will write 2 / 4 in the RHS which will be equal to half.

[00:02:58]In LHS 4x² / 4 x² - 4x / 4 x in RS we have half.

[00:03:10]Let's say this is equation number one.

[00:03:15]Now we will write required expression E.

[00:03:20]So if I will write here e equal to then we can write 16 x^ 4 - 16 xq - 12 x² + 12 x + 5.

[00:03:45]Now we are going to take 16 x² common from these two terms.

[00:03:51]So we will write 16 x² common in the bracket we'll write x² - x from next two terms we are going to take -12 common.

[00:04:08]So we are going to get the same bracket x² - x once again.

[00:04:15]Then we will write the remaining constant + 5.

[00:04:21]Now from equation number one we have x² - x half which we are going to apply here and here.

[00:04:34]So we will get 16 x² * half - 12 * half + 5 16 / 2 is 8 12 / 2 is 6. So we can write here 8 x² - 6 + 5 e will be equal to 8 x² - 6 + 5 which will be equal to 8 x² - 1.

[00:05:28]Now we have equation number one which is x² - x =/ now we will take - x to the rhs.

[00:05:43]So we can write here x² = x + 1 /2 which we are going to apply over here.

[00:05:57]So we will get expression value 8 x² -1 in place of x² we will write x + 1 / 2 then we have -1.

[00:06:16]Now we have to simplify.

[00:06:18]So we will multiply 8 with x 8 x 8 with half 4 then we have minus 1 so we will get 8 x 4 - 1 is + 3.

[00:06:36]So far expression value will be equal to 8 x + 3. Now we have to plug in x = <unk>3 + 1 / 2.

[00:06:49]So we will write here expression e = 8x + 3.

[00:06:59]Here x is a square <unk>3 + 1 / 2.

[00:07:09]So we'll find E value equal to 8 * in place of X we'll be writing square<unk> 3 + 1 / 2 + 3.

[00:07:28]Now we will expand or we can write here 8 / 2 * square<unk> 3 + 1 + 3 8 / 2 is 4. So we will write 4 * square<unk> 3 + 1 + 3.

[00:07:56]Now we have to simplify. We are going to get 4 square<unk> 3 + 4 + 3.

[00:08:08]So we can write our final answer here.

[00:08:12]4<unk>3 + 7 7 + 4 <unk>3 or 4<unk>3 + 7 will be our final answer. I hope friends you will like this video. Thank you so very much for watching. Do not forget to like, share and subscribe. Bye-bye. Till next video. Good luck. Take care. Bye-bye.