I like the way you rewrote the equation to a symmetric form❤. The algebra can be simplified by use of the binomial formula, with odd terms cancelling and even terms doubling. (t-1)^4+ (t+1)^4 = 2 (t^4 + 6 t^2 +1) = 706 (t^2 + 3)^2 = 9 + 706/2 -1 = 361 = 19^2 and so on...
9 and 11 are both near 10. Rewrite perturbed eqn as (X + 10)^4 ~=~ 353 Sqrt twice by rough mental arithmetic X + 10 ~=~ 4.2 Test x as -6 in original eqn.
By inspection, 3^4=81, 5^4=625. So x=-6 and -14. Why is this difficult? Surely not any university entrance assessment? Most mathematically inclined 14 yr olds (or younger) would enjoy this problem.
Not liking this shit method put it like (X+ 9 ) (X+9) ( x+9) ( x+9) = x^2 + 18x + 81 * x^2 + 18x + 81(x+11) ^4= 706 Muktiply both x^2+ 18x+ 81 and x^2+18x+ 81 , and show what's the product HEE HEE 💀 😂✌
A, b, T substitution all rubbish,NO concept there, all memory of substuting at right step, am not memorising, Explain like my way mentioned easy only concept HEE HEE 💀😂✌
I like the way you rewrote the equation to a symmetric form❤.
The algebra can be simplified by use of the binomial formula, with odd terms cancelling and even terms doubling.
(t-1)^4+ (t+1)^4 = 2 (t^4 + 6 t^2 +1) = 706
(t^2 + 3)^2 = 9 + 706/2 -1 = 361 = 19^2
and so on...
Yes his expansion was painful. I agree with using binomial formula or deriving coefficients from Pascal's triangle
@@dan-florinchereches4892 totally agreed.
9 and 11 are both near 10.
Rewrite perturbed eqn as
(X + 10)^4 ~=~ 353
Sqrt twice by rough mental arithmetic
X + 10 ~=~ 4.2
Test x as -6 in original eqn.
By inspection, 3^4=81, 5^4=625. So x=-6 and -14. Why is this difficult? Surely not any university entrance assessment? Most mathematically inclined 14 yr olds (or younger) would enjoy this problem.
Smart people states foolish, foolish people states smart.
You state smart.
The problem is, it would be catastrophic to prove they are the ONLY solutions, better off to solve it
You must first say the domain of x. which is common in ALL your videos.
I appreciate you pointing that out! I’ll make sure to be more specific about the domain in the future. 🙏
@@superacademy247 thank you.
You're welcome 💕🔥🥰✅
Also, (x+9)^4 - 81= 625 - (x+11)^4 where 625 = 5^4 and 81 = 3^4.
Not liking this shit method
put it like
(X+ 9 ) (X+9) ( x+9) ( x+9)
= x^2 + 18x + 81 * x^2 + 18x + 81(x+11) ^4= 706
Muktiply both x^2+ 18x+ 81 and x^2+18x+ 81 , and show what's the product HEE HEE 💀 😂✌
A, b, T substitution all rubbish,NO concept there, all memory of substuting at right step, am not memorising, Explain like my way mentioned easy only concept HEE HEE 💀😂✌
Oxford University Software DevOps Entrance Exam: (x + 9)⁴ + (x + 11)⁴ = 706, x =?
706 > (x + 11)⁴ > (x + 9)⁴ > 0 or 706 > (x + 9)⁴ > (x + 11)⁴ > 0
Let: y = x + 10; x + 9 = y - 1, x + 11 = y + 1, (y - 1)⁴ + (y + 1)⁴ = 706
(y ± 1)⁴ = y⁴ ± 4y³ + 6y² ± 4y + 1, (y - 1)⁴ + (y + 1)⁴ = 2(y⁴ + 6y² + 1) = 706
y⁴ + 6y² + 1 = 353, y⁴ + 6y² - 352 = 0, (y² - 16)(y² + 22) = 0
y² - 16 = 0; y² = 16 = 4²; y = ± 4 or y² + 22 = 0, y² = - 22; y = ± i√22
y = x + 10 = ± 4, x = - 6; x = - 14; y = ± i√22 = x + 10, x = - 10 ± i√22
Answer check:
x = - 6: (x + 9)⁴ + (x + 11)⁴ = 3⁴ + 5⁴ = 706; Confirmed
x = - 14: (- 5)⁴ + (- 3)⁴ = 5⁴ + 3⁴ = 706; Confirmed
x = - 10 ± i√22: (± i√22 + 1)⁴ + (± i√22 - 1)⁴ = 2[(i√22)⁴ + 6(i√22)² + 1]
= 2[(22)(22 - 6) + 1] = 2(353) = 706; Confirmed
Final answer:
x = - 6; x = - 14; Two complex value roots, if acceptable;
x = - 10 + i√22 or x = - 10 - i√22