Find x value | A nice exponential problem || mathematics

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[pkyoutubepage]

M² - M³ = 150
M²(1 - M) = 25(6)
1 - M = 6
M = -5✅
Sub the value of M in equation 1️⃣,
(-5)²(1-(-5)) = 25(6)
25(6) = 25(6)
150 = 150
Hence, proved💯

[HappyTheAptera]

This is easy to do in your head. Once you realize that 5² = 25 and 5³ = 125 and 25 + 125 = 150, you wonder how you can put them together. Since (-5)³ = -125, the answer HAS to be -5!

[ddebabratadatta]

Since we have a cubic function, there must be 3 solutions. Hence only deriving M = - 5 is not a complete answer. Other two solutions have to be worked out.

[calvinmasters]

It has to be a negative. A neg^2 is positive and a neg^3 is negative. Makes sense.
Try -2. (-2)^2 - (-2^3)= 4 + * = 12
Try -3. 3^2 + 3^3 = 36
Try -5. 5^2 + 5^3 = 25 + 125 = 150

[satrajitghosh]

m^3 - m ^2 + 150 = 0
m^3 + 125 -m^2 + 25 = 0
( m + 5) ( m^2 - 5 m + 25 - m + 5) = 0
(m + 5) ( m^2 - 6 m + 30) = 0
only feasible solution in real domain is m = - 5

[pas]

Let M^2=a. Then the equation becomes a-a√a=150. Now

a-150=a√a. Squaring both sides we get (a-150)^2=a^3. By bringing RHS to left side. You (a-150)^2=a^3. You have a^3-a^2+22500=0. It is a cubic equation . You can get the value of a. Then root of that gives you the value of M.

[ravikishoremvk]

First of all her, I appreciate her method of doing. As it is a bit advanced problem, a training must be given in the following way. Clearly M not equal to 0 and +1 & -1 (verify by substitution. Also M cannot be between -1 and +1 as RHS is 150. So M must be either > 1 or < -1. Once again if M > 1 cannot satisfy the problem by substituting any value > 1. Hence M < -1. NOTE THAT ALL THE ABOVE EXPLANATION CAN BE DONE EASILY IN THE BACK OF ONE’S MIND. Not a big deal. A training towards mathematics must be like that.
Now our answer is M < -1. Now guess work starts (also called inspection). 150 = 6x5^2 or 125 +25 =5^3 +5^2 —-> M = -5
Please accept her method also. 👍

[sundaramsadagopan]

Simple way:
(m^2)(1-m)=(25)(6), m^2=25, m=+/- 5, 1-m=6, -m=6-1, m=-5

[sunnysharma]

By inspection method and solving we get m=-5

[KamleshVermaVerma-eo]

Easy Square me se quib ghatana hai.. It means.. Number negative hai

[raajikrish]

Why complicate like this? It is very simple. When M+5 multiplied by something is 0, take that something to the other side, the value becomes 0 (0 divided by anything is 0). Hence M+5 is 0 and hence M is -5.

[Dカーズ]

Another Solution

M³-M²+150=0
(M+5)(M²-6M+30)=0
※By factor theorem

M+5=0 ⇔ M=-5

M²-6M+30=0
↓
※Completing the square
(M-3)²-9+30=0
(M-3)²=-21
M-3=±√21 i
M=3±√21 i

Answer
M=-5, 3±√21 i

[ahmadhabibi]

can be verificated complex roots to eq above ?

[pi]

M^2(1-M)=150=25*6
M^2=25
1-M=6
M=1-6=-5

[Gatheringinfowithus]

(5.68)3 - (5.68)2. =150
The value of M= 5.68

[GeoRedtick]

Times like this make me glad I know the rational zeros theorem and synthetic division.

[VanshShrivastava_art]

Can we solve this equation by these step

First take m common then m(m-m^2)= 150
m=150/(m-m^2)
Then put this value and easily get m

[michallesz]

You don't understand why DELTA is calculated. In your solution, delta is less than zero, which means that the equation has no solutions, and you want to prove otherwise by force. I don't think you understand the result of delta. Delta is calculated to see if the equation has solutions. When delta is less than zero, it means that the equation has no solutions, because the graph of the function does not intersect the X axis. After all, you equated the equation to 0, so Y has the value 0, which means that only those x are solutions that touch the x axis. And since delta is negative, there is no x that would touch the x axis.

[md.nazmulislammilky]

Last part of this solution make with complex, it can do by the middle term method

[MuhammadArshad-gjqk]

Encourage this young girl and learn from her.
Don’t give your own solutions. If you know more just stay put. Thank you friends.