Nice Algebra Math Simplification | Find the Value of X

Nice Algebra Math Simplification | Find the Value of X

[@ajitandyokothakur7191]

There is a better and more elegant way of solving this equation: Sqrt(x) + SQRT(x-9) = 9 or, SQRT(x-9) = 9 - SQRT(X). Squaring both sides, x - 9 = 81 + x - 18SQRT(x); Transposing and simplifying: -90 = - 18SQRT(x),. Dividing both sides by -18, 6 = SQRT(x). Squaring both sides and transposing we get x = 25. Ans. Dr. Ajit Thakur (USA).

[@Haxor6666]

Rising function and injective for x>=9 results it has a single unique solution which you can notice as x=25.

[@ajitandyokothakur7191]

Sorry about a mistake in my workout, I wrote 6 = SQRT(x), it should have been 5 = SQRT(x) instead. Dr. Thakur.

[@mkadx2136]

حليتها عن طريق التخمين لأنه من الواضح ان x عدد موجب وأكبر من 9 فقمت بتجريب 16 وثم 25 فكانت الإجابة 25، لكن دائم عندما استخدم هذه الطريقة للحل اشعر بانها ليست صحيحة لأنه في هذه الحالة الذي كتب السؤال اختار عدد صحيحا، لكن ماذا لو اختار عدد غير صحيح؟

[@sumitchakraborty4010]

Not a good method to solve this problem and it is also lengthy.

[@henritraccard4762]

more simple solution (sqr(x)+sqr(x-9))*(sqr(x)-sqr(x-9))/(sqr(x)-sqr(x-9))=9 (x-x+9)/(sqr(x)-sqr(x-9))=9 9/(sqr(x)-sqr(x-9))=9 1/(sqr(x)-sqr(x-9))=1 sqr(x)-sqr(x-9)=1 and we have now sqr(x)+sqr(x-9)=9 sqr(x)-sqr(x-9)=1 _________________ 2*sqr(x)=10 sqr(x)=5 and finally x=25