Question

please answer this question​

Answer 1

Please check the image to understand the question.

We need to prove,

5$AB^{2}$ = 5$AC^{2}$ + $BC^{2}$

Now, the black colored stuff represent $AB^{2}$,

the red colored stuff represents $AC^{2}$.

The green, is the difference of the two above.

Using Pythagoras theorem we find $AB^{2}$, and substitute the give condition,

DB = 3/2 CD

then, we find $AC^{2}$, and subtract the two.

Now, we have after taking the '-' common from the equation in the image,

$AB^{2}$ - $AC^{2}$ = 5/4 $CD^{2}$

Multiply 5 to get to the required equation.

5$AB^{2}$ - 5$AC^{2}$ = 25/4 $CD^{2}$ ------------- I

Now, $BC^{2}$ = $[CD + 3/2 CD]^{2}$ = 25/4 $CD^{2}$

Hence, I can be deduced as,

5$AB^{2}$ = 5$AC^{2}$ + $BC^{2}$

Hence, proved.