Please tell me the soloution of the following:

factorize, x2-y2-x-y, squareroot of 3x2+11x+6squareroot3, x2+12/35+1/35

if 2 medians of the trianggle are equal then prove that it is an isosceles triangle.

divide squareroot162bysquare root 2

prove square root 7 is an irrational number.

(1)

(i) x² – y² – x – y

= (x² – y²) – (x + y)

= (x + y) (x – y) – (x + y)

= (x + y) (x – y – 1)

(iii)

(2)

Given: In ΔABC, BD and CE are medians intersecting at F and BD = CE.

To Prove: AB = AC

Proof: We know that centroid divides the median in the ratio 2 : 1

Now BD = CF

⇒BF = CF

Now in ΔBFC

∠FBC = ∠FCB  (Angles opposite to equal sides)  .........(1)

In ΔBEC and ΔCDB

CE = BD (Given)

∠ECB = ∠DBC  (from (1))

BC = BC (Common)

So ΔBEC ≅ ΔCDB (by SAS congruency rule)

⇒BE = CD (C.P.C.T.)

⇒2BE = 2CD

⇒AB = AC

(3)

(4) Here is the link for the similar answer to your query.

https://www.meritnation.com/ask-answer/question/prove-that-root-5-is-an-irrartional-number-using-theory/polynomials/1131526