find value of y : [60/(10+y)]+9=65/(10-y)
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Answer:
i tried but i think i did it
Step-by-step explanation:
WRONG
Verified answer
Answer:
>>> [tex]\bold{ \sf{5 \: and \: \dfrac{ - 170}{9} }}[/tex]
Step-by-step explanation:
Given Equation ,
We have to find ,
Solution :
[tex] \sf{ \longmapsto \: \: \: \dfrac{60}{10 + y} + 9 = \dfrac{65}{10 - y} }[/tex]
[tex] \sf{ \longmapsto \: \: \: \dfrac{60}{10 + y} - \dfrac{65}{10 - y} + 9 = 0} [/tex]
[tex] \sf{ \longmapsto \: \: \: \dfrac{60}{10 + y} - \dfrac{65}{10 - y} = - 9} [/tex]
Taking LCM :
[tex] \sf{ \longmapsto \: \: \: \dfrac{60(10 - y) - 65(10 + y)65}{(10 + y)(10 - y)} = - 9} [/tex]
[tex] \sf{ \longmapsto \: \: \: 60(10 - y) - 65(10 + y)65 = - 9(10 + y)(10 - y)} [/tex]
[tex] \sf{ \longmapsto \: \: \: 600 - 60y - 650 - 65y = - 9(10 + y)(10 - y)} [/tex]
[tex] \sf{ \longmapsto \: \: \: - 125y - 50 = - 9 \{(10) {}^{2} -( y) {}^{2} \} } [/tex]
[tex] \sf{ \longmapsto \: \: \: \cancel{ -} (125y + 50) = \cancel{ -} 9 \{(10) {}^{2} -( y) {}^{2} \} } [/tex]
[tex] \sf{ \longmapsto \: \: \: 125y + 50 = 9 \{(10) {}^{2} -( y) {}^{2} \}}[/tex]
[tex] \sf{ \longmapsto \: \: \: 125y + 50 = 9 \{(100 -( y) {}^{2} \}}[/tex]
[tex] \sf{ \longmapsto \: \: \: 125y + 50 = 900 -9y {}^{2} }[/tex]
[tex] \sf{ \longmapsto \: \: \: 9y {}^{2} + 125y + 50 - 900 = 0 } [/tex]
[tex] \sf{ \longmapsto \: \: \: 9y {}^{2} + 125y -850 = 0 } [/tex]
Splitting the middle term i.e. 125y into 170y - 45y :
[tex] \sf{ \longmapsto \: \: \: 9y {}^{2} + 170y - 45y - 850 = 0 } [/tex]
[tex] \sf{ \longmapsto \: \: \: y (9y +170) - 5 (9y + 170) = 0 } [/tex]
[tex]\sf{ \longmapsto \: \: \: ( y - 5) (9y + 170) = 0 } [/tex]
#Values of y are :
[tex]\sf{ \longmapsto \: \: \: y - 5 = 0 } [/tex]
[tex]\sf{ \longmapsto \: \: \: \underline{ \boxed{ \bold{y = 5} }}} \: \: \: \bigstar[/tex]
and ,
[tex]\sf{ \longmapsto \: \: \: 9y + 170 = 0 } [/tex]
[tex]\sf{ \longmapsto \: \: \: 9y = - 170 } [/tex]
[tex]\sf{ \longmapsto \: \: \: \underline{ \boxed{ \bold{y = \dfrac{ - 170}{ \: \: 9} } }}} \: \: \: \bigstar[/tex]