Question

If 3m - n = 5 and mn = 6, then
9m2 + n2 = ?​

Answer 1

$\underline{\boxed{\bold{ \bigstar \; Question \; \bigstar }}}$

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➠ If 3m - n = 5 and mn = 6, then 9m² + n² = ?

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$\underline{\boxed{\bold{ \bigstar \; Important \; Information \; \bigstar }}}$

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❏ Algebraic identities that are frequently used in mathematics to simply our calculations and get our answer in short period of time.

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❏ Here are some important identities used in daily mathematics.

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$\star \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \boxed{ \bold {:\longmapsto (a+b)^2 = a^2+ b^2 + 2ab}}$

$\star \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \boxed{ \bold {:\longmapsto (a-b)^2 = a^2+ b^2 - 2ab}}$

$\star \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \boxed{ \bold {:\longmapsto (a+b+c)^2 = a^2+ b^2 + c^2 + 2ab + 2bc + 2ca}}$

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$\underline{\boxed{\bold{ \bigstar \; Answer \; \bigstar }}}$

Let's Start !

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❖ Here is your answer :)

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☯ We will use second identities mentioned below.

$\star \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \boxed{ \bold {:\longmapsto (a-b)^2 = a^2+ b^2 - 2ab}}$

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$:\implies (3m-n)^2 = (3m)^2+ (n)^2 - 2(3m)(n)$

$:\implies (3m-n)^2 = 9m^2+ n^2 - 6mn$

$:\implies (5)^2 = 9m^2+ n^2 - 6(6)$

$:\implies 25 = 9m^2+ n^2 - 36$

$:\implies 9m^2+ n^2 = 25 + 36$

$:\implies 9m^2+ n^2 = 61$

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$\boxed{\boxed{\bold{\therefore Value \; of \; 9m^2+ n^2 = 61 }}}$

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Hope this helps u.../

【Brainly Advisor】

Answer 2

Answer:

➠ If 3m - n = 5 and mn = 6, then 9m² + n² = ?

\; \; \; \;

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

\; \; \; \;

\underline{\boxed{\bold{ \bigstar \; Important \; Information \; \bigstar }}}

★ImportantInformation★

\; \; \; \;

❏ Algebraic identities that are frequently used in mathematics to simply our calculations and get our answer in short period of time.

\; \; \; \;

❏ Here are some important identities used in daily mathematics.

\; \; \; \;

\star \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \boxed{ \bold {:\longmapsto (a+b)^2 = a^2+ b^2 + 2ab}}⋆

:⟼(a+b)

2

=a

2

+b

2

+2ab

\star \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \boxed{ \bold {:\longmapsto (a-b)^2 = a^2+ b^2 - 2ab}}⋆

:⟼(a−b)

2

=a

2

+b

2

−2ab

\star \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \boxed{ \bold {:\longmapsto (a+b+c)^2 = a^2+ b^2 + c^2 + 2ab + 2bc + 2ca}}⋆

:⟼(a+b+c)

2

=a

2

+b

2

+c

2

+2ab+2bc+2ca

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\; \; \; \;

\underline{\boxed{\bold{ \bigstar \; Answer \; \bigstar }}}

★Answer★

Let's Start !

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\; \; \; \;

❖ Here is your answer :)

\; \; \; \;

☯ We will use second identities mentioned below.

\star \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \boxed{ \bold {:\longmapsto (a-b)^2 = a^2+ b^2 - 2ab}}⋆

:⟼(a−b)

2

=a

2

+b

2

−2ab

\; \; \; \;

:\implies (3m-n)^2 = (3m)^2+ (n)^2 - 2(3m)(n):⟹(3m−n)

2

=(3m)

2

+(n)

2

−2(3m)(n)

:\implies (3m-n)^2 = 9m^2+ n^2 - 6mn:⟹(3m−n)

2

=9m

2

+n

2

−6mn

:\implies (5)^2 = 9m^2+ n^2 - 6(6):⟹(5)

2

=9m

2

+n

2

−6(6)

:\implies 25 = 9m^2+ n^2 - 36:⟹25=9m

2

+n

2

−36

:\implies 9m^2+ n^2 = 25 + 36:⟹9m

2

+n

2

=25+36

:\implies 9m^2+ n^2 = 61:⟹9m

2

+n

2

=61

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\; \; \; \;

\boxed{\boxed{\bold{\therefore Value \; of \; 9m^2+ n^2 = 61 }}}

∴Valueof9m

2

+n

2

=61

\; \; \; \;

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Hope this helps u.../