Question

if X square + Y square into a square + b square equal to a + b y for square prove that x by y equal to y by b​

Answer 1

Answer:

PROVED

Step-by-step explanation:

Given:

(x² + y²) (a² + b²) = (ax + by)²

Step-by-step explanation:

(x² + y²) (a² + b²) = (ax + by)²

= x²a² + x²b² + y²a² + y²b² = a²x² + b²y² + 2abxy

= x² + b² + y²a² - 2abxy = 0

= (xb - ya)² = 0                                                                 (1)

                                          (a² - b²) = a² - 2ab + b²        (2)

On comparing (1) and (2).

we get xb = ya

hence,

x/y=y/b

#SPJ3

Answer 2

Answer:

$\Huge\bold\pink{Proved \: down}$

Step-by-step explanation:

$\huge{As\: we \: know}$

$(a+b) {}^{2} =a {}^{2} +b {}^{2} +2ab,(a−b) {}^{2} =a {}^{2} +b {}^{2} −2ab$

$Given (x {}^{2} +y {}^{2} )(a {}^{2} +b {}^{2} )=(ax+by) {}^{2}$

$x {}^{2} (a {}^{2} +b {}^{2} )+y {}^{2} (a {}^{2} +b {}^{2} )=(ax) {}^{2} +(by) {}^{2} +2(ax)(by)$

$\implies \: a {}^{2} x {}^{2} +b {}^{2} x {}^{2} +a {}^{2} y {}^{2} +b {}^{2} y {}^{2} =a {}^{2} x {}^{2} +b {}^{2} y {}^{2} +2abxy$

$⟹b {}^{2} x {}^{2} +a {}^{2} y {}^{2} =2abxy$

$⟹(bx) {}^{2} +(ay) {}^{2} - 2(bx)(ay) = 0$

$(bx - ay) {}^{2} = 0$

$bx = ay$

$\frac{x}{a} = \frac{y}{b}$

$\huge\underline\frak\red{Hence \: proved}$