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Multiply eqn with(√45^ 2- x^2) gives45^2+ x^2= 126(√45^2-x^2) let a= √(45^ 2- x^2)givesa^2+ 123a- 4050= 04050= 150× 27 hence a= 27; -150 a> 0 so only 27 valid. Hence x^2= 45^2 - 27^2= 72×18= (36)^2 orX = + -36 solns.
That's a great way to approach the problem! 🎉
👍 excellent
Sqrt[((45+x)^3)/(45-x)]+Sqrt[((45-x)^3)/(45+x)]=246 x=±36 x=±15Sqrt[91]i
With respect, there is no need to find a and b since, (ab)^2=27^2=45^2-x^2, hence, x^2=45^2-27^2=(45-27)(45+27)=(18)(72)=9(2)9(8)=9^2x4^2, hence, x=9(4)=36 or -36
(135+x^3/(45 ➖ x)^2+(17275 ➖ x^3)/(135+x^3)=135x^3/(2025 ➖ x^2)+{x^0+x^0 ➖ x^0+x^0 ➖ x^0+x^0 ➖ }/135x^3=135+x^3/{x^0+x^0 ➖ x^0+x^0 ➖}+x^3/135x^3 ={135x^3/x^2+x^3/135x^3}=135x^6/135x^5=1x^1.1 1x^1 (x ➖ 1x+1).
(1^1 ➖x)^1/45 ➖ x +(1^1 ➖ x)^1/(1^1)^1 (1/1^1).(/1^1) (x ➖ 1x+1).
Multiply eqn with(√45^ 2- x^2) gives
45^2+ x^2= 126(√45^2-x^2) let a= √(45^ 2- x^2)gives
a^2+ 123a- 4050= 0
4050= 150× 27 hence
a= 27; -150 a> 0 so only 27 valid. Hence x^2= 45^2 - 27^2= 72×18= (36)^2 or
X = + -36 solns.
That's a great way to approach the problem! 🎉
👍 excellent
Sqrt[((45+x)^3)/(45-x)]+Sqrt[((45-x)^3)/(45+x)]=246 x=±36 x=±15Sqrt[91]i
With respect, there is no need to find a and b since, (ab)^2=27^2=45^2-x^2, hence, x^2=45^2-27^2=(45-27)(45+27)
=(18)(72)=9(2)9(8)=9^2x4^2, hence, x=9(4)=36 or -36
(135+x^3/(45 ➖ x)^2+(17
275 ➖ x^3)/(135+x^3)=135x^3/(2025 ➖ x^2)+{x^0+x^0 ➖ x^0+x^0 ➖ x^0+x^0 ➖ }/135x^3=135+x^3/{x^0+x^0 ➖ x^0+x^0 ➖}+x^3/135x^3 ={135x^3/x^2+x^3/135x^3}=135x^6/135x^5=1x^1.1 1x^1 (x ➖ 1x+1).
(1^1 ➖x)^1/45 ➖ x +(1^1 ➖ x)^1/(1^1)^1 (1/1^1).(/1^1) (x ➖ 1x+1).