Question

a. (x+14)² = x² + (x+7)²

b. (x+5)² = 6² + (x+3)²

Answer 1

A.
$( x+14)^{2} = x^{2} + (x+7)^{2} \\ x^{2} +28x+196= x^{2} + x^{2} +14x+49 \\ x^{2} + x^{2} - x^{2} +14x-28x-196+49=0 \\ x^{2} -14x-147=0$
Δ$=196+588=784$
$x'= \frac{14+28}{2} \\ x'=21$
$x''= \frac{14-28}{2} \\ x''=-7$

B.
$(x+5)^{2} = 6^{2} + (x+3)^{2} \\ x^{2} +10x+25=36+ x^{2} +6x+9 \\ x^{2} - x^{2} +10x-6x=36+9-25 \\ 4x=20 \\ x= \frac{20}{4} \\ x=5$