1)Simplify by using identity-:
Answers
Answer:
1st question answer is 2
2nd question answer is 13 or -13
3rd answer is 73.
Answer:
)856×856+167×167(856+167)2+(856−167)2
{(a + b)}^{2} + {(a - b)}^{2} = 2( {a}^{2} + {b}^{2} )(a+b)2+(a−b)2=2(a2+b2)
so \: \frac{2( {856}^{2} + {167}^{2} ) }{( {856}^{2} + {167}^{2} )} = 2so(8562+1672)2(8562+1672)=2
1st question answer is 2
2)\:a^2+b^2+c^2= > 792)a2+b2+c2=>79
and \: ab +bc+ca= > 45andab+bc+ca=>45
{(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ca)(a+b+c)2=a2+b2+c2+2(ab+bc+ca)
so \: {(a + b + c)}^{2} = 79 + 2(45) = 79 + 90 = 169so(a+b+c)2=79+2(45)=79+90=169
{(a + b + c)} = 13 \: or \: - 13(a+b+c)=13or−13
2nd question answer is 13 or -13
3)x + y + z = 143)x+y+z=14
{x}^{2} + {y}^{2} + {z}^{2} = 50x2+y2+z2=50
{(x + y + z)}^{2} = {x}^{2} + {y}^{2} + {z}^{2} + 2(xy + yz + xz)(x+y+z)2=x2+y2+z2+2(xy+yz+xz)
{14}^{2} = 50 + 2(xy + yz + xz)142=50+2(xy+yz+xz)
196 - 50 = 2(xy + yz + zx)196−50=2(xy+yz+zx)
146 = 2(xy + yz + zx)146=2(xy+yz+zx)
(xy + yz + zx) = 73(xy+yz+zx)=73
3rd answer is 73.