Hi All ..Really Sorry that I did not up date this for a long long time, though I am pursuing the objectives of this blog at other web sites...
Now that I have a wealth of information thanks to  various students who contacted me for help, over the past few years , I now propose to give that through this blog for use of all students in need ...
Here we go ..

IN GENERAL WE HAVE …A SYMMETRIC MATRIX A =
A=
B	C
C	D
IF ITS SQUARE ROOT IS X THEN LET
X=			X^2=
P	Q		P^2+QR	PQ+QS
R	S		RP+SR	RQ+S^2
P^2+QR=B……………………1
Q[S+P]=C………………………2
R[S+P]=C…………………….3
S^2+QR=D
EQN. 2 / EQN. 3 , GIVES ...Q = R …………….4
THIS PROVES THAT X THE SQUARE ROOT OF A
IS A SYMMETRIC MATRIX …………..PROVED …..
A=
13	10
10	17
X^2=A……LET X BE			X^2=
P	Q		P^2+QR	PQ+QS
R	S		RP+SR	RQ+S^2
P^2+QR=13……………………1
Q[S+P]=10………………………2
R[S+P]=10…………………….3
S^2+QR=17
EQN. 2 / EQN. 3 , GIVES ...Q = R …………….4
THIS PROVES THAT X THE SQUARE ROOT OF A
IS A SYMMETRIC MATRIX …………..PROVED …..
EQN. 1 - EQN.2 , GIVES
S^2-P^2=4
[S+P][S-P]=4………………………………….5
SOLVING BY XL GOAL SEEK WE GET …
P	Q	R	S
0.70642	3.535671	3.535671	2.121092
HENCE X =
0.70642	3.535671
3.535671	2.121092
SINCE ALL PRINCIPAL MINORS OF X ARE POSITIVE
X IS POSITIVE DEFINITE

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the base b and corresponding height h of a triangle are integers. A 2x2 square is inscribed in the triangle with one side on the given base, and vertices on the other two sides. what are the possible values of the pair (b,h)?