Question

Find the value of x which: (x+4)²-(x-5)²=9 *​

Answer 1

Answer:

x=1

Step-by-step explanation:

x^2+8x+16-(x^2-10x+25)=9

x^2+8x+16-x^2+10x-25=9

18x-9=9

18x=9+9

18x=18

x=1

Answer 2

Answer :-

$\implies\sf (x+4)^2-(x-5)^2=9$

Using the identities :-

• $\sf ( a + b )^2 = a^2 + b^2 + 2ab$
• $\sf ( a - b )^2 = a^2 + b^2 - 2ab$

$\implies\sf x^2 + 4^2 + 2 ( x ) ( 4) - [ x^2 + 5^2 - 2 ( x )(5) ] = 9$

$\implies\sf x^2 + 16 + 8x - [ x^2 + 25 - 10x ] = 9$

$\implies\sf x^2 + 16 + 8x - x^2 - 25 + 10x = 9$

$\implies\sf \cancel{x^2} - \cancel{x^2} + 16 - 25 + 8x + 10x = 9$

$\implies\sf -9 + 8x + 10x = 9$

$\implies\sf 18x - 9 = 9$

$\implies\sf 18x = 9 + 9$

$\implies\sf 18x = 18$

$\implies\sf x = \dfrac{18}{18}$

$\implies\sf x = 1$

Value of x = 1

Verification :-

$\sf LHS = (x+4)^2-(x-5)^2$

$\implies\sf LHS = ( 1+4)^2 - (1-5)^2$

$\implies\sf LHS = 5^2 - (-4)^2$

$\implies\sf LHS = 25 - 16$

$\implies\sf LHS = 9$

$\sf RHS = 9$

LHS = RHS

Hence verified.