Question

X square + Y square is equals to 7 x y then 2
log x + Y is equals to log x + log Y + lock 2 log 3​

Answer 1

Answer:

$x^{2} + y^{2} = 7xy$

$\implies x^{2} + y^{2} + 2xy = 7xy + 2xy$

$\implies ( x + y )^{2} = 9xy$

$\implies ( x + y )^{2} = 3^{2}xy$

$\implies log( x + y )^{2} = log (3^{2}xy)$

$\implies 2log( x + y )= log (3^{2})+log xlog y$

$\boxed { \pink { log m^{n} = n log m }}$

$\boxed { \orange { log mn= log m + log n }}$

$\implies 2log( x + y )= 2 log 3+log xlog y$

$Hence\: proved$

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Answer 2

1.STEP: Xsquare+ysquare=7x

2.STEP: adding 2xy on both sides.

3.STEP: xsquare+ysquare+2xy=7xy+2xy.

4.STEP: [X+Y]whole square=9xy

5.STEP: adding log on both sides

6.STEP log[X+Y]whole square=log9xy

7.STEP:2log[X+Y]=logx+logy+log9

8.STEP: logx+logy+log3square

9.STEP:logx+logy+2log3.

.............Hence proved...............